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

Start with

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

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

then for (2) calculate \(\displaystyle \frac{df}{dy}\), 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.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217
 
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 :)
 
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?
 
What you need is the "chain rule": the derivative of \(\displaystyle e^{f(x)}\) with respect to x is \(\displaystyle e^{f(x)}\frac{df}{dx}\).

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

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