What is the derivative of #f(t) = (t^2-lnt, t^2-cos^2t ) #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer Narad T. Oct 21, 2016 #dy/dx=(t(2t+sint))/(2t^2-1)# Explanation: Let's call #x(t)=t^2-lnt# then #x('t)=dx/dt=2t-1/t=(2t^2-1)/t# and #y(t)=t^2-cos^2t# Then #y'(t)=dy/dt=2t-2cost*-sint=2t+sin2t# And finally #dy/dx=(dy/dt)/(dx/dt)=(2t +sint)/((2t^2-1)/t)# #dy/dx=(t(2t+sint))/(2t^2-1)# 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 1405 views around the world You can reuse this answer Creative Commons License