How do you implicitly differentiate #6=ylny-e^x-e^y#?
1 Answer
Jan 8, 2016
Explanation:
Find the derivative of each part.
#d/dx(6)=0#
Use the product rule and chain rule here.
#d/dx(ylny)=y'lny+y(1/y)y'=y'lny+y'#
#d/dx(e^x)=e^x#
Chain rule:
#d/dx(e^y)=y'e^y#
Thus, the derivative of the entire implicit equation is
#0=y'lny+y'-e^x-y'e^y#
Solve for
#e^x=y'(lny+1-e^y)#
#y'=e^x/(lny+1-e^y)=dy/dx#