What is the derivative of #f(t) = (t +e^t, e^t-tcost ) #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer 1s2s2p Feb 1, 2018 #(dy)/(dx)=(e^t+tsint)/(1+e^t)# Explanation: #x=t+e^t# #y=e^t-tcost# #(dy)/(dx)=(dy)/(dt)-:(dx)/(dt)# #(dy)/(dt)=d/dt[e^t-tcost]# #color(white)((dy)/(dt))=d/dt[e^t]-d/dt[tcost]# #color(white)((dy)/(dt))=e^t+tsint# #(dx)/(dt)=d/dt[t+e^t]# #color(white)((dx)/(dt))=d/dt[t]+d/dt[e^t]# #color(white)((dx)/(dt))=1+e^t# #(dy)/(dx)=(e^t+tsint)/(1+e^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 1396 views around the world You can reuse this answer Creative Commons License