What is the derivative of #f(t) = (t-lnt, t^2sint ) #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer moutar Jan 10, 2016 #f'(t)=(y'(t))/(x'(t))# #x'(t)=1-1/t = (t-1)/t# #y'(t) = 2tsint+t^2cost# #f'(t) = (2tsint+t^2cost)/((t-1)/t)# #f'(t) = (t^2(2sint+tcost))/(t-1)# 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 1995 views around the world You can reuse this answer Creative Commons License