What is the derivative of #f(t) = (t^2-sint , t-e^t ) #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer Shwetank Mauria Apr 5, 2018 #(df)/(dx)=(1-e^t)/(2t-cost)# Explanation: Derivative of #f(t)=(x(t),y(t))# is given by #(df)/(dx)=((dy)/(dt))/((dx)/(dt))# As #x(t)=t^2-sint#, #(dx)/(dt)=2t-cost# and #y(t)=t-e^t#, #(dy)/(dt)=1-e^t# Hence #(df)/(dx)=(1-e^t)/(2t-cost)# 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 1286 views around the world You can reuse this answer Creative Commons License