Derivative of Parametric Functions

Key Questions

• How do you find the second derivative of a parametric function?

  Let `{(x=x(t)),(y=y(t)):}`.

  First Derivative

  `{dy}/{dx}={{dy}/{dt}}/{{dx}/{dt}}={y'(t)}/{x'(t)}`

  Second Derivative

  `{d^2y}/{dx^2}=d/{dx}[{y'(t)}/{x'(t)}]=1/{{dx}/{dt}}{d}/{dt}[{y'(t)}/{x'(t)}]`

  by Quotient Rule,

  `=1/{x'(t)}cdot{y''(t)x'(t)-y'(t)x''(t)}/{[x'(t)]^2}`

  `={y''(t)x'(t)-y'(t)x''(t)}/{[x'(t)]^3}`

  I hope that this was helpful.

  Wataru · · Oct 2 2014
• How do you find `dy/dx` for the curve `x=t*sin(t)`, `y=t^2+2` ?

  To find the derivative of a parametric function, you use the formula:

  `dy/dx = (dy/dt)/(dx/dt)`, which is a rearranged form of the chain rule.

  To use this, we must first derive `y` and `x` separately, then place the result of `dy/dt`over `dx/dt`.

  ---

  `y=t^2 + 2`

  `dy/dt = 2t` (Power Rule)

  ---

  `x=tsin(t)`

  `dx/dt = sin(t) + tcos(t)` (Product Rule)

  ---

  Placing these into our formula for the derivative of parametric equations, we have:

  `dy/dx = (dy/dt)/(dx/dt) = (2t)/(sin(t)+tcos(t))`

  Collin C. · 1 · Aug 28 2014
• How do you find derivatives of parametric functions?

  For the parametric equations

  `{(x=x(t)),(y=y(t)):}`,

  we can find the derivative

  `{dy}/{dx}={{dy}/{dt}}/{{dx}/{dt}}={y'(t)}/{x'(t)}`.

  Wataru · · Sep 20 2014

• How do you find the second derivative of a parametric function?
• How do you find derivatives of parametric functions?
• How do you find `dy/dx` for the curve `x=t*sin(t)`, `y=t^2+2` ?
• How do you find the equation of the tangent to the curve `x=t^4+1`, `y=t^3+t` at the point where `t=-1` ?
• How do you find `(d^2y)/(dx^2)` for the curve `x=4+t^2`, `y=t^2+t^3` ?
• How do you find parametric equations of a tangent line?
• How do you find parametric equations for the tangent line to the curve with the given parametric equations `x=7t^2-4` and `y=7t^2+4` and `z=6t+5` and (3,11,11)?
• How do you find the equation of a line tangent to the curve at point `t=-1` given the parametric equations `x=t^3+2t` and `y=t^2+t+1`?
• How do you differentiate the following parametric equation: `x(t)=t^3-5t, y(t)=(t-3)`?
• How do you differentiate the following parametric equation: `x(t)=lnt, y(t)=(t-3)`?
• How do you differentiate the following parametric equation: `x(t)=lnt/t, y(t)=(t-3)^2`?
• How do you differentiate the following parametric equation: `x(t)=lnt-t, y(t)=(t-3)^2`?
• How do you differentiate the following parametric equation: `x(t)=e^t-t, y(t)=1-t^2`?
• How do you differentiate the following parametric equation: `x(t)=e^t-1/t, y(t)=1-t^2`?
• How do you differentiate the following parametric equation: `x(t)=1/t, y(t)=1/(1-t^2)`?
• How do you differentiate the following parametric equation: `x(t)=t/(t-4), y(t)=1/(1-t^2)`?
• How do you differentiate the following parametric equation: `x(t)=t/(t-4), y(t)=1+t`?
• How do you differentiate the following parametric equation: `x(t)=1/t, y(t)=lnt`?
• How do you differentiate the following parametric equation: `x(t)=e^(t^2-t) , y(t)=lnt`?
• How do you differentiate the following parametric equation: `x(t)=e^(t^2-t) , y(t)=t^2-t`?
• How do you differentiate the following parametric equation: `x(t)=te^t , y(t)=e^t`?
• How do you differentiate the following parametric equation: `x(t)=te^-t , y(t)=e^t/t`?
• How do you differentiate the following parametric equation: `x(t)=te^t , y(t)=e^t/t`?
• How do you differentiate the following parametric equation: `x(t)=t-te^t , y(t)=e^t`?
• How do you differentiate the following parametric equation: `x(t)=t^2-te^t , y(t)=e^(3t)`?
• How do you differentiate the following parametric equation: `x(t)=(t+3t^2)e^t , y(t)=t/e^(3t)`?
• How do you differentiate the following parametric equation: `x(t)=(1-t)/e^t , y(t)=t/e^(3t)`?
• How do you differentiate the following parametric equation: `x(t)=e^t/(t+t), y(t)=t-e^(3t)`?
• How do you differentiate the following parametric equation: `x(t)=e^t/(t+t)^2-1, y(t)=t-e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=e^t/(t+t)^2-t, y(t)=t-e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=e^t-t, y(t)=sint`?
• How do you differentiate the following parametric equation: `x(t)=cost, y(t)=sint`?
• How do you differentiate the following parametric equation: `x(t)=tcost, y(t)=tsint`?
• How do you differentiate the following parametric equation: `x(t)=t, y(t)=t`?
• How do you differentiate the following parametric equation: `x(t)=cos^2t, y(t)=sint/t`?
• How do you differentiate the following parametric equation: `x(t)=cos^2t, y(t)=sin2t`?
• How do you differentiate the following parametric equation: `x(t)=t^2cos^2t, y(t)=tsint`?
• How do you differentiate the following parametric equation: `x(t)=t-cos^2t, y(t)=tsint`?
• How do you differentiate the following parametric equation: `x(t)=t-cos2t, y(t)=tsin^2t`?
• How do you differentiate the following parametric equation: `x(t)=t^2+cos2t, y(t)=t-sint`?
• How do you differentiate the following parametric equation: `x(t)=t^2+tcos2t, y(t)=tsint`?
• How do you differentiate the following parametric equation: `x(t)=sqrt(t^2+tcos2t), y(t)=t^2sint`?
• How do you differentiate the following parametric equation: `x(t)=-t^2+tcost, y(t)=t^2sint`?
• How do you differentiate the following parametric equation: `x(t)=e^t-t, y(t)=tant-sect`?
• How do you differentiate the following parametric equation: `x(t)=e^t-t, y(t)=e^tsect`?
• How do you differentiate the following parametric equation: `x(t)=e^tcost-t, y(t)=e^t-sint`?
• How do you differentiate the following parametric equation: `x(t)=e^t-cost-t, y(t)=e^t-tsint`?
• How do you differentiate the following parametric equation: `x(t)=t^2-t, y(t)=e^t+cost`?
• How do you differentiate the following parametric equation: `x(t)=t^2-t, y(t)=t^3-t^2+3t`?
• How do you differentiate the following parametric equation: `x(t)=te^t-2t, y(t)=-3t^3-2t^2+3t`?
• How do you differentiate the following parametric equation: `x(t)=-te^t-2t, y(t)= 3t^3-4t`?
• How do you differentiate the following parametric equation: `x(t)=-te^t+t, y(t)= 3t^3-4t`?
• How do you differentiate the following parametric equation: `x(t)=-te^t+t, y(t)= 3t^2+2t`?
• How do you differentiate the following parametric equation: `x(t)=-e^t+4t, y(t)= 3t^2+2t`?
• How do you differentiate the following parametric equation: `x(t)=-e^t-4t, y(t)= -5t^2+2`?
• How do you differentiate the following parametric equation: `x(t)=-3e^t-2t, y(t)= -5t^2+2`?
• How do you differentiate the following parametric equation: `x(t)=-3e^t-2t, y(t)= -5t^2-e^(4t)`?
• How do you differentiate the following parametric equation: `x(t)=-3e^t-4t, y(t)= -5t^2-e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=-2te^t+4t, y(t)= -5t^2-e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=-2te^t+4t, y(t)= -2t^2-3e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=te^t+5t, y(t)= t^2-3e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=-te^t+t, y(t)= -2t^2-2te^(t)`?
• How do you differentiate the following parametric equation: `x(t)=-t-e^t, y(t)= -2t^2-2t^3e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=(lnt)^2, y(t)= -2t^2-2t^3e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=sqrt(t-2), y(t)= t^2-2t^3e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=tsqrt(t^2-1), y(t)= t^2-e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=tsqrt(t^2-1), y(t)= sqrt(t^2-e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=t/sqrt(t^2-1), y(t)= sqrt(t^2-e^(t)`?
• How do you differentiate the following parametric equation: `x(t)=t^3-t, y(t)= 1-sint`?
• How do you differentiate the following parametric equation: `x(t)=t, y(t)= 1-tcost`?
• How do you differentiate the following parametric equation: `x(t)=-3t/(1-t), y(t)= 1-tcost`?
• How do you differentiate the following parametric equation: `x(t)=t/2, y(t)= 1-t-cost`?
• How do you differentiate the following parametric equation: `x(t)=lnt, y(t)= tcost`?
• How do you differentiate the following parametric equation: `x(t)=lnt-t, y(t)= tcos^2t`?
• How do you differentiate the following parametric equation: `x(t)=lnt-2t, y(t)= cos^2t`?
• How do you differentiate the following parametric equation: `x(t)=1-lnt, y(t)= cost-t^2`?
• How do you differentiate the following parametric equation: `x(t)=t-lnt, y(t)= cost-sint`?
• How do you differentiate the following parametric equation: `x(t)=tlnt, y(t)= cost-sin^2t`?
• How do you differentiate the following parametric equation: `x(t)=tlnt, y(t)= cost-tsin^2t`?
• How do you differentiate the following parametric equation: `x(t)=tlnt, y(t)= t^3cost-tsin^2t`?
• How do you differentiate the following parametric equation: `x(t)=e^tsint, y(t)= tcost-tsin^2t`?
• How do you differentiate the following parametric equation: `x(t)=te^tsint, y(t)= tcost-sin^2t`?
• How do you differentiate the following parametric equation: `x(t)=te^t, y(t)= t^2-e^(t-1)`?
• How do you differentiate the following parametric equation: `x(t)=t-(t+1)e^t, y(t)= t^2-e^(t-1)`?
• How do you differentiate the following parametric equation: `x(t)=(t+1)e^t, y(t)= t-e^(t-1)`?
• How do you differentiate the following parametric equation: `x(t)=(t+1)e^t, y(t)= (t-2)^2+t`?
• How do you differentiate the following parametric equation: `x(t)=(t+1)^2+e^t, y(t)= (t-2)^2+t`?
• How do you differentiate the following parametric equation: `x(t)=3(t+1)^2+2e^t, y(t)= (t+2)^2+t^2`?
• How do you differentiate the following parametric equation: `x(t)=(t-1)^2-e^t, y(t)= (t+2)^2+t^2`?
• How do you differentiate the following parametric equation: `x(t)=te^t-lnt, y(t)= t^3e^t-t^2+t`?
• How do you differentiate the following parametric equation: `x(t)=t-e^(t^2-t+1), y(t)= te^(t-t^2)`?
• How do you differentiate the following parametric equation: `x(t)=t-e^(t^2-t+1)/t, y(t)= t^2-e^(t-t^2)`?
• How do you differentiate the following parametric equation: `x(t)=t-5, y(t)= t^2`?
• How do you differentiate the following parametric equation: `x(t)=3t-1, y(t)= t^2-t+4`?
• How do you differentiate the following parametric equation: `x(t)=-t-2, y(t)= t^2/(-t+4`?
• How do you differentiate the following parametric equation: `(t-5t^3,3t^4-t^3)`?
• How do you differentiate the following parametric equation: `(t-t^3,3/t^4-t^3)`?
• How do you differentiate the following parametric equation: `(sint,cost-t)`?
• How do you differentiate the following parametric equation: `(sint,tcost-pit)`?
• How do you differentiate the following parametric equation: `(tsec(t/3-pi),t cos(pi-t))`?
• How do you differentiate the following parametric equation: `(3sin(t/6-pi/12), 2tcos(pi/3-t/8))`?
• How do you differentiate the following parametric equation: `(3t-sin(t/3-pi/4), 2tcos(pi/3-t/4))`?
• How do you differentiate the following parametric equation: `(t-tsin(t/2+pi/3), 2tcos(pi/2-t/3))`?
• How do you differentiate the following parametric equation: `(t-tsin(t/3), -tcos(pi/2-t/3))`?
• What is the slope of `f(t) = (t^2-tsqrtt,t/2)` at `t =3`?
• What is the slope of `f(t) = (t-2t^2,t)` at `t =-1`?
• What is the slope of `f(t) = (t-2t+4,t^2)` at `t =0`?
• What is the slope of `f(t) = (t+1,t)` at `t =0`?
• What is the slope of `f(t) = (t+1,t^3)` at `t =1`?
• What is the slope of `f(t) = (t-1,t^3)` at `t =1`?
• What is the slope of `f(t) = (t-1,t+3)` at `t =1`?
• What is the slope of `f(t) = (t^2-t,t+3)` at `t =1`?
• What is the slope of `f(t) = (t^2+2t,t-3)` at `t =1`?
• What is the slope of `f(t) = (t^2+2t,2t-3)` at `t =-1`?
• What is the slope of `f(t) = (-4t^2+2t,2t)` at `t =-1`?
• What is the slope of `f(t) = (t-2,2t)` at `t =-1`?
• What is the slope of `f(t) = ((t-2)^3,2t)` at `t =-1`?
• What is the derivative of `f(t) = (t-sint , cost )`?
• What is the derivative of `f(t) = (t-sint , cost/t^2 )`?
• What is the derivative of `f(t) = (t/sint , cost/t^2 )`?
• What is the derivative of `f(t) = (t/sint , t^2-t^3cost )`?
• What is the derivative of `f(t) = (tsint , t^2-tcost )`?
• What is the derivative of `f(t) = (tsint , t^2-t tant )`?
• What is the derivative of `f(t) = (tcos^2t , t^2-t sect )`?
• What is the derivative of `f(t) = (tcos^2t , t^2-t /sect )`?
• What is the derivative of `f(t) = (tcos^2t , t^2-cost )`?
• What is the derivative of `f(t) = (tcos^2t , t^2sin^2t-cost )`?
• What is the derivative of `f(t) = (te^t , t^2sin^2t-cost )`?
• What is the derivative of `f(t) = (te^t , e^tcost )`?
• What is the derivative of `f(t) = (te^t +e^t, e^t-cost )`?
• What is the derivative of `f(t) = (e^t/t +e^t, e^t-cost )`?
• What is the derivative of `f(t) = (e^t/t +e^t, e^t-tcost )`?
• What is the derivative of `f(t) = (t +e^t, e^t-tcost )`?
• What is the derivative of `f(t) = (t +e^t, te^t-sint )`?
• What is the derivative of `f(t) = (t +e^t, te^t-t^2+t )`?
• What is the derivative of `f(t) = (t +te^t, e^t-t^2+t )`?
• What is the derivative of `f(t) = (1-te^t, t^2+t )`?
• What is the derivative of `f(t) = (2-te^t, 2t^2+5t )`?
• What is the derivative of `f(t) = (2t-3te^t, 2t^2+3t )`?
• What is the derivative of `f(t) = (2t-3te^t, 2t^2-t )`?
• What is the derivative of `f(t) = (2t-e^t, 2t^2-t )`?
• What is the derivative of `f(t) = (e^(t^2)-e^t, 2t^2-t )`?
• What is the derivative of `f(t) = (e^(t^2)-e^t, 2t^2-4t )`?
• What is the derivative of `f(t) = (e^(t^2-1)-e^t, 2t^2-4t )`?
• What is the derivative of `f(t) = (e^(t^2-1)-t, 2t^2-4t )`?
• What is the derivative of `f(t) = (e^(t^2-1)-t, 2t^3-4t )`?
• What is the derivative of `f(t) = (e^(t^2-1)-t, -t^3-4t )`?
• What is the derivative of `f(t) = (e^(t^2-1)+3t, -t^3+t )`?
• What is the derivative of `f(t) = (lnt, -3t^3+5t )`?
• What is the derivative of `f(t) = (lnt, 3t^2+5t )`?
• What is the derivative of `f(t) = (tlnt, 3t^2+5t )`?
• What is the derivative of `f(t) = (tlnt, 3t^2-t )`?
• What is the derivative of `f(t) = (t-lnt, te^t )`?
• What is the derivative of `f(t) = (t-lnt, tsint )`?
• What is the derivative of `f(t) = (t-lnt, t^2sint )`?
• What is the derivative of `f(t) = (t-lnt^2, t^2sint )`?
• What is the derivative of `f(t) = (t-lnt^2, t^2-sint )`?
• What is the derivative of `f(t) = (t^2-lnt, t^2-sint )`?
• What is the derivative of `f(t) = (t^2-lnt, t^2-sin^2t )`?
• What is the derivative of `f(t) = (t^2-lnt, t^2-cos^2t )`?
• What is the derivative of `f(t) = ((lnt)^2-t, t^2cost )`?
• What is the derivative of `f(t) = ((lnt)^2-t, tcost )`?
• What is the derivative of `f(t) = ((lnt)^2-t, tsint )`?
• What is the derivative of `f(t) = ((lnt)^2-t, tcsct )`?
• What is the derivative of `f(t) = ((lnt)^2-t, tsect )`?
• What is the derivative of `f(t) = ((lnt)^2-t, sec(1-t) )`?
• What is the derivative of `f(t) = (1-t , sec(1-t) )`?
• What is the derivative of `f(t) = (1-e^t , sec(1-t) )`?
• What is the derivative of `f(t) = (e^(1-t) , tan^2t )`?
• What is the derivative of `f(t) = (t^3e^(1-t) , tan^2t )`?
• What is the derivative of `f(t) = (t^3-e^(1-t) , tan^2t )`?
• What is the derivative of `f(t) = (t^3-te^(1-t) , t^2-6t+e^t )`?
• What is the derivative of `f(t) = (t^3-te^(1-t) , t^2-t+te^t )`?
• What is the derivative of `f(t) = (t^3-e^(3t-1) , t^2+te^t )`?
• What is the derivative of `f(t) = (t^3-e^(3t-1) , 3t^2+2e^t )`?
• What is the derivative of `f(t) = (t^3-e^(3t-1) , -t^2-e^t )`?
• What is the derivative of `f(t) = (t^3-e^(3t-1) , t-e^t )`?
• What is the derivative of `f(t) = (t^2-2e^(3t-1) , t-e^t )`?
• What is the derivative of `f(t) = (t^2-2e^(t-1) , t-e^t )`?
• What is the derivative of `f(t) = (t^2-sint , t-e^t )`?
• What is the derivative of `f(t) = (t^2-sint , t-1 )`?
• What is the derivative of `f(t) = (t^2-sint , 1/(t-1) )`?
• What is the derivative of `f(t) = (t^2-sint , 1/(t^2-1) )`?
• What is the derivative of `f(t) = (1/(3t) , t/(5t-4) )`?
• What is the derivative of `f(t) = (1/(3t+2) , t/(t^2-1) )`?
• What is the derivative of `f(t) = (t/(t+2) , t/(t^2-1) )`?
• What is the derivative of `f(t) = (t/(t+1) , t/(4t^2-t) )`?
• What is the derivative of `f(t) = (t/(t+1) , 1/(t^2-t) )`?
• What is the derivative of `f(t) = (-1/(t+1) , e^(2t-1) )`?
• What is the derivative of `f(t) = (t/(t+1) , te^(2t-1) )`?
• What is the derivative of `f(t) = (t^2-1 , te^(2t-1) )`?
• What is the derivative of `f(t) = (t^2-1 , t^2-e^(2t-1) )`?
• What is the derivative of `f(t) = (t^2-1 , t^2+1 -e^(2t^2-2) )`?
• What is the derivative of `f(t) = (t^2-1 , te^(2t^2-2) )`?
• What is the derivative of `f(t) = (t^2+1 , e^(2t^2-2) )`?
• What is the derivative of `f(t) = (t^2+1 , e^(-t^2-t) )`?
• What is the derivative of `f(t) = (t^2+1 , e^(1-t) )`?
• What is the derivative of `f(t) = (t^2+1 , t-e^(1-t) )`?
• What is the derivative of `f(t) = (t^2-t , t^2-e^(1-t)/t^3 )`?
• The motion of the particle is given parametrically by `x(t)=3t^2-3`, `y(t)=2t +2` for t is greater than or equal to 0, how do you find the speed of the particle at t=1?
• Question #5cb24
• Question #34c6f
• Question #f6b13
• Question #7fdfd
• Question #bdbad
• How do you find the equations of the tangent and normal of the curve at `x=t^2`, `y=t+3`, `t=1`?
• How do you find the equations of the tangents to `5x^2-4y^2=4` at those points where the curve is cut by `5x-2y=4`?
• How do you find dy/dx given `x = t^2 - 2t` and `y = t^4 - 4t`?
• How do you find d/dt given `y=t^3 - 3t` and `x=t^2`?
• How do you find cartesian equation the parametric equations of a circle are `x=cos theta -4` and `y=sin theta + 1`?
• How do you find the vector equation and the parametric equations of the line that passes through the points A (3, 4) and B (5, 5)?
• How do you find the parametric equation of a line in R3 that passes through P(1,1,1) and is orthogonal to both the lines x=3-t, y= -1+4t, z = -2t and x=2+2t, y=1+t, z=-2+3t where t is any real number?
• How do you find an equation for the plane that contains the line with parametric equations `l=(8 - 7t, -5 - 2t , 5 - t)` and is parallel to the line with parametric equations `x=3 + t, y=-7 + 9t, z=8 - 6t`?
• The ellipse `((x^2)/(2^2) + (y^2)/(3^2))=1` can be drawn with what parametric equations?
• Given 2x -3y + z - 6 = 0, how do you get a vector equation from this scalar or a parametric equations?
• How do you convert the parametric equation to rectangular form `x = e^t`, `y = e^(-t)`?
• How do you find the parametric equation for y if `x = e^t` for the line passing through the points (2,1) and (-2,3)?
• A soccer ball kicked at the goal travels in a path given by the parametric equations: x=50t; `y=-16t^2+32t`, At what two times will the ball be at a height of 6ft.?
• A soccer ball kicked at the goal travels in a path given by the parametric equations: x=50t; `y=-16t^2+32t`, Suppose the ball enters the goal at a height of 5ft. How far away from the goal was the kicker?
• How do you turn the parametric equations into a Cartesian equation x = t -1 y = -3 t?
• How do you find two different parametric equations for rectangular equation given: y = 6x - 1?
• How do you find the parametric equations of each line in space the line that intersects (4,5,-2) and is parallel to the z-axis?
• How do you find the parametric equations of line through the origin and parallel to the line determined by x = 2t, y = 1 - t, z = 4 + 3t?
• How do you find the parametric equations of line that passes through the points (1, 3, 2) and ( -4, 3, 0)?
• How do you find d²y/dx² when x=1+2cost y=1+3sint?
• Given that a curve C is represented parametrically by x=t²/2 + 3t y=t²-2t how do you find the value of dy/dx and show that d²2y/dx²=8/(t+3)^3 and Show that C has only one stationary point and that this is a minimum?
• Given `y=3x^2 - 2`, why/how is `x= sqrt(3)*t` and `y = t^2 -2` the parametric equations?
• The parametric equation of a curve are `x=t+e^-t`, `y=1-e^-t`, where t takes all real values. How do you find dy/dx in terms of t, and hence find the value of t, for which the gradient of the curve is 1, giving your answer in logarithmic form?
• Given x = cost y=sin2t, how do you find the dy/dx terms parameter t and find the values parameter t points dy/dx = 0?
• The curve has a parametric equation of `x=(t^3)-12t` and `y=3(t^2)`, how would you find the two points the parameter t=2 crosses the curve?
• How do you transform parametric equations into Cartesian form: x= 3 + 2 cost and y= 1 + 5sint?
• How do you write the pair of parametric equations as a single equation in x and y given x=7t-7 and `y=7t^2-3`?
• A Curve (C) Has Parametric Equations x=3cost and y=cos2t and find the coordinates on the point on the curve where the gradient is 1?
• How do you determine the intersection between parametric curves `(t^2+2t,-3t^2+5t)` and `(-2t^2+4t,t^2+2t)`?
• Question #3e542
• Question #12fa5
• Find the derivative of `1/(-sint)`?