How do you differentiate the following parametric equation: # x(t)=-e^t-4t, y(t)= -5t^2+2 #?
1 Answer
Sep 3, 2017
# dy/dx = ( 10t ) / ( e^t+4 )#
Explanation:
We have:
# x(t) = -e^t-4t #
# y(t) = -5t^2+2 #
Differentiating each equation wrt
# x'(t) = -e^t-4 #
# y'(t) = -10t #
By the chain rule rule we have:
# dy/dx = (dy/dt) / ( dx/dt) #
# \ \ \ \ \ \= ( y'(t) ) / ( x'(t) )#
# \ \ \ \ \ \= ( -10t ) / ( -e^t-4 )#
# \ \ \ \ \ \= ( 10t ) / ( e^t+4 )#
