Another implicit differentiation

[afcwestwarrior]

e^x^y = x +y

ok i know i am suppost to use the chain rule and the product rule

so x+y is 1 +1 if u find the derivatives, but e^x^2 is confusing me, what is u and what is n

i think u= e^x^2 and n= y is that possible for n to equal y, this problem is confusing

 

[dextercioby]

So you need to find \frac{dy}{dx}. Assume

F(x,y)=e^x^y-x-y

What are
\frac{\partial F}{\partial x} \ , \frac{\partial F}{\partial y}

equal to ?

 

[HallsofIvy]

e^x^y = x +y

ok i know i am suppost to use the chain rule and the product rule

so x+y is 1 +1 if u find the derivatives, but e^x^2 is confusing me, what is u and what is n

i think u= e^x^2 and n= y is that possible for n to equal y, this problem is confusing

Your notation is ambiguous. Is e^x^2 supposed to be (e^x)^2 or e^(x^2). I would guess the latter since (e^x)^2 can be written more simply as e^(2x) but you should make it clear.

Oh, and what in the world do you mean by "so x+ y is 1+ 1"? If you mean "the derivative of x+ y is 1+ 1", that is wrong. What variable are you differentiating with respect to? Since you mention the "chain rule" I would guess that x and y are functions of some third variable- again you should tell us that and not make us guess. (Okay, I now notice that the title of this was "another implicit differentiation! But we still don't know whether we are to assume y is a function of x or vice-versa.)

I surely can't answer your question "what is n" because there is no "n" in your formula! Again, I can guess that you mean the "n" in the formula (xⁿ)'= n x^n-1 but I can't be sure.

PLEASE restate the problem exactly as it given! (And don't just tell us it is "e^x^y= x+y". That's not even a problem. It may well be one of a list of problems in which the "instructions" [what you are to assume and what you are to do] are at the top of the list.)

It might help you to think about how you would differentiate x^x or, more generally, x^f(x), since y is a function of x. (Do you remember "logarithmic differentiation"?)