How do you differentiate the following parametric equation: # x(t)=(t+1)^2+e^t, y(t)= (t-2)^2+t#? Calculus Parametric Functions Derivative of Parametric Functions 1 Answer ali ergin May 27, 2016 #d y=((2(t-2)+1) /(2(t+1)+e^t*l n e))*d x# Explanation: #(d x)/(d t)=2*(t+1)*1+e^t*l n e=2(t+1)+e^t*l n e# #(d y)/( d t)=2*(t-2)*1+1=#2(t-2)+1 #(d y)/(d x)=(d y)/(d t)*(d t)/(d x)=[2(t-2)+1] /(2(t+1)+e^t*l n e)# #d y=((2(t-2)+1) /(2(t+1)+e^t*l n e))*d x# 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 1202 views around the world You can reuse this answer Creative Commons License