What is the derivative of #f(t) = (t-lnt^2, t^2-sint ) #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer 1s2s2p May 23, 2018 #dy/dx=(2t^2-tcost)/(t-2)# Explanation: Given #x=f(t),y=g(t)# #dy/dx=(dy/dt)/(dx/dt)# #dy/dt=g'(t)=2t-cost# #dx/dt=f'(t)=1-(2t)/t^2=1-2/t# #dy/dx=(2t-cost)/(1-2/t)=(2t-cost)/((t-2)/t)=(2t^2-tcost)/(t-2)# Answer link Related questions 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... 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... How do you find the equation of a line tangent to the curve at point #t=-1# given the parametric... 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) #? See all questions in Derivative of Parametric Functions Impact of this question 1428 views around the world You can reuse this answer Creative Commons License