Differentiation of exp(xy) wrt x

[j-lee00]

Please help

Differentiate exp(xy) w.r.t x

Thanks

 

[neutrino]

You need to show your work/attempt.

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

 

[j-lee00]

differentiate implicitly

exp(xy) = 0

i thought i would write it out but i don't know how to write the mathmatical symbols on screen

 

[neutrino]

i thought i would write it out but i don't know how to write the mathmatical symbols on screen

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

differentiate implicitly

exp(xy) = 0

Do you know how to differentiate the exponential function?

 

[j-lee00]

exp(x)*exp(y)*y'+exp(y)+exp(x)

 

[Moo Of Doom]

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))?

 

[j-lee00]

i don't know i think that's my problem

 

[j-lee00]

i presume f'(x)*exp(f(x))

 

[Moo Of Doom]

That's correct!

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

 

[j-lee00]

ah thanks just forgot this simple derivation

 

[Mute]

differentiate implicitly

exp(xy) = 0

i thought i would write it out but i don't know how to write the mathmatical symbols on screen

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.

 

[j-lee00]

i didnt give the whole equation because i could take the derivatives of the other functions
the full equation is x + y + exp(xy) = 0