# Thread: how to differentiate e^(x/y) with respect to 1) x and 2) y

1. ## how to differentiate e^(x/y) with respect to 1) x and 2) y

how to differentiate e^(x/y) with respect to
1) x and
2) y

2. Originally Posted by itsmusa7
how to differentiate e^(x/y) with respect to
1) x and
2) y
Start with

$\displaystyle f(x,y) = e^{\frac{x}{y}}$

Now for (1) calculate $\frac{df}{dx}$, treating y as constant

then for (2) calculate $\frac{df}{dy}$, treating x as constant

Please share your work with us .

If you are stuck at the beginning tell us and we'll start with the definitions.

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3. ## Re: how to differentiate e^(x/y) with respect to 1) x and 2) y

Thank You sir for helping me, but I think I haven't got the help I needed. I needed the process of differentiating e^(x/y) with respect to 1) x and 2) y, especially " y ", because I know the process of differentiating it with respect to " x ", but never did it with respect to " y ". And I think I've posted my question in the wrong category. Sorry for that. I have read your forum rules " before posting " and I'll be careful in future. Thanks

4. Originally Posted by itsmusa7
Thank You sir for helping me, but I think I haven't got the help I needed. I needed the process of differentiating e^(x/y) with respect to 1) x and 2) y, especially " y ", because I know the process of differentiating it with respect to " x ", but never did it with respect to " y ". And I think I've posted my question in the wrong category. Sorry for that. I have read your forum rules " before posting " and I'll be careful in future. Thanks
suppose you had:

z = e^(a/x) ................ where 'a' is a constant

can you calculate dz/dx?

5. What you need is the "chain rule": the derivative of $e^{f(x)}$ with respect to x is $e^{f(x)}\frac{df}{dx}$.

Now, differentinating $e^{x/y}$ with respect to x, f(x)= x/y. What is the derivative of x/y with respect to x?

Differentiating $e^{x/y}$ with respect to y, $f(y)= x/y= xy^{-1}$. What is the derivative of $xy^{-1}$ with respect to y?

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