Question

Implicit Differentiation?

Answer 1

\[\ln(xy) =e ^{x+y}\]

Answer 2

The question is asking for dy/dx. I have this so far, but I can't figure out how to solve for y'.\[\frac{ y+xy' }{ xy } = e^{x+y}(1+y')\]

Answer 3

\[\Rightarrow\frac{ y}{xy}+\frac{xy' }{ xy } = e^{x+y}+e^{x+y}y'\]

Answer 4

You might try the Implicit Function Theorem, if you know it:

So

\(f(x,y) = \ln(xy) - e ^{x+y}\)

and then \(\dfrac{dy}{dx} = - \dfrac{f_x}{f_y}\)