How do you differentiate the following parametric equation: # x(t)=te^t+5t, y(t)= t^2-3e^(t) #? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer Ratnaker Mehta Sep 23, 2016 #dy/dx=((t+1)e^t+5)/(2t-3e^t).# Explanation: By Defn., #dy/dx=(dy/dt)/(dx/dt)# #y=y(t)=t^2-3e^t rArr dy/dt=d/dt(t^2-3e^t)=d/dt(t^2)-d/dt(3e^t)# #=2t-3e^t# #x=x(t)=te^t+5t rArr dx/dt=d/dt(te^t+5t)=d/dt(te^t)+d/dt(5t)# #=td/dt(e^t)+e^td/dt(t)+5=te^t+e^t+5=(t+1)e^t+5# #:. dy/dx=((t+1)e^t+5)/(2t-3e^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 1264 views around the world You can reuse this answer Creative Commons License