How do you differentiate the following parametric equation: # x(t)=tcost, y(t)=tsint #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer VinÃcius Ferraz Nov 21, 2015 #alpha'(t) = (x', y') (t)# Explanation: Differentiate #alpha = (x,y)# on #t#. #x' = t'cost + t cos' t = 1 cos t + t (-sin t)# #y' = t' sin t + t sin' t = 1 sin t + t (cos t)# #alpha'(t) = ((cos t - t sin t), (sin t + t cos t))# 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 5260 views around the world You can reuse this answer Creative Commons License