What is the derivative of #f(t) = (t-lnt^2, t^2sint ) #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer Shwetank Mauria Feb 22, 2018 #(dy)/(dx)=(2t^2sint+t^3cost)/(t-2)# Explanation: Derivative #(dy)/(dx)# of #f(t)=(x(t),y(t))# is given by #((dy)/(dt))/((dx)/(dt))# As #y(t)=t^2sint#, #(dy)/(dt)=2tsint+t^2cost# and as #x(t)=t-lnt^2#, #(dx)/(dt)=1-(2t)/t^2=1-2/t# Hence #((dy)/(dt))/((dx)/(dt))=(2tsint+t^2cost)/(1-2/t)# = #(2t^2sint+t^3cost)/(t-2)# 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 1418 views around the world You can reuse this answer Creative Commons License