Differential with x, y, and base e

[karmic28]

Hi! I was having trouble with this problem:
Find dy/dx if xe^y+4=xy

My thought was to take the natural log of both sides, but I still had trouble with the 4. I think I need to separate x and y to either side, but I'm super stuck. Any help would be very appreciated!

 

[Steven G]

The natural log of the left hand side is simply the natural log of the left hand side which is ln(xe^y+4)

I have a question for you: If f(x) = e^x, would you use natural logs to find f'(x)?

Hint: Just use the product and sum rule to find the derivative of the left hand side.

 

[BigBeachBanana]

I think I need to separate x and y to either side, but I'm super stuck. Any help would be very appreciated!

It's not necessary to separate them, but if you prefer:
[math]xe^y+4=xy\\ xe^y-xy+4=0\\ x(e^y-y)+4=0\\[/math]Continue...

 

[topsquark]

Hi! I was having trouble with this problem:
Find dy/dx if xe^y+4=xy

My thought was to take the natural log of both sides, but I still had trouble with the 4. I think I need to separate x and y to either side, but I'm super stuck. Any help would be very appreciated!

Just take the implicit derivative of both sides. For example: [imath]\dfrac{d}{dx} \left ( x e^y \right ) = e^y + x e^y \dfrac{dy}{dx}[/imath] by the product and chain rules. Then solve for dy/dx.

-Dan