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