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
[tex]\displaystyle f(x,y) = e^{\frac{x}{y}}[/tex]
Now for (1) calculate [tex]\frac{df}{dx}[/tex], treating y as constant
then for (2) calculate [tex]\frac{df}{dy}[/tex], 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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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
What you need is the "chain rule": the derivative of [tex]e^{f(x)}[/tex] with respect to x is [tex]e^{f(x)}\frac{df}{dx}[/tex].
Now, differentinating [tex]e^{x/y}[/tex] with respect to x, f(x)= x/y. What is the derivative of x/y with respect to x?
Differentiating [tex]e^{x/y}[/tex] with respect to y, [tex]f(y)= x/y= xy^{-1}[/tex]. What is the derivative of [tex]xy^{-1}[/tex] with respect to y?
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