How to solve by implicit differentiation e^xy+x^2-y^2=10?

Question

anonymous · Answer

x^2+e^(x y) = y^2+10

anonymous · Answer

How? 10 is a non-issue because it's a constant I thought...

anonymous · Answer

I didn't solve it, I just showed you another way that it's written.

zepdrix · Answer

$$\large e^{xy}+x^2-y^2=10$$Is the y in the exponent as I have it written above? It's a little unclear in the original post.

anonymous · Answer

Yes, thats it. I mainly need to ffigure out how to work with the e$$e^{xy}$$

zepdrix · Answer

So the derivative of $e^x$ would give us $e^x$ right?
The only difference here will be, we'll have to apply the chain rule, multiplying by the derivative of the exponent.

zepdrix · Answer

$$\large \left(e^{xy}\right)' \qquad = \qquad e^{xy}(xy)'$$
Understand what I mean? The exponential gave us the same thing back, but now we have to apply the chain rule.

zepdrix · Answer

From here, we'll need to apply the product rule.

anonymous · Answer

Thanks. I knew the basic details, but I wasn't sure how to go about the e. Big help.