How do you differentiate the following parametric equation: # x(t)=t^2+cos2t, y(t)=t-sint #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer Eddie Jun 21, 2016 #\frac{dy}{dx} = \frac{1 - cos t}{2(t - sin 2t)}# Explanation: #\frac{dx}{dt} = 2t - 2 sin 2t# #\frac{dy}{dt} = 1 - cos t# #\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{1 - cos t}{2(t - sin 2t)}# 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 1457 views around the world You can reuse this answer Creative Commons License