Differentiation of exp(xy) wrt x

You need to show your work/attempt.

And is y a function of x, or are x and y independent variables?

 

Okay, then, use a (') to show a derivative. For example, y' will be the derivative of y w.r.t x.

Do you know how to differentiate the exponential function?

 

It sort of (but not quite) looks like you're differentiating exp(x)exp(y) rather than exp(xy). Those two are not equal.

What's the derivative of exp(f(x))?

 

That's correct!

Now substitute f(x) = xy. What do you get?

 

There is a problem with your implicit equation there: exp(xy) is never zero, it only approaches it asymptotically. (So technically, the surface doesn't exist, so neither does the derivative!)

But otherwise, you can just do what you did to get a derivative for other surfaces of exp(xy), e.g. exp(xy) = 5, which will produce a surface, and so the derivative will exist and you'd get the same derivative as if you tried to differentiate exp(xy) = 0.