How can I 'evaluate' the following derivative and simplify it ?

xy^2 = 3^(y/ln x) + sin^2 x

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- August 24th 2010, 05:24 AMSangrealImplicit Differentiation
How can I 'evaluate' the following derivative and simplify it ?

xy^2 = 3^(y/ln x) + sin^2 x - August 24th 2010, 09:09 AMlvleph
I assume you are taking the derivative with respect to x? If so you need to use the chain rule, i.e. .

To start you off

.

Also, if then

I hope that helps. - August 24th 2010, 09:21 AMyeKciM

you don't need to do it like that... (i assume that your last " y' " is derivated by the x :D ) it's much easier (for more complex problems) to just get the constant (in this case y) out ...

this :

is being used for derivate something like this (where are two functions )

that what you did there is like that for (2x^2) for derivate on "x" you do :D:D:D:D:D that's to much work to be done, especially when we have constant on our hands :D:D:D:D

sorry i don't have intention to be rude or something :D but to do derivation of function and constant like derivation of two functions ... that's not wrong but not needed at all :D - August 24th 2010, 09:26 AMlvleph
Except that you are assuming that y is a constant with respect to x and I was not assuming this. Because there was no statement of dependence of y on x it is more correct to assume dependence and then if there is no dependence we can just say and everything simplifies to your case.

- August 24th 2010, 09:43 AMyeKciM
- August 24th 2010, 09:46 AMlvleph
No, it is not. Here is a good example. .

- August 24th 2010, 10:02 AMyeKciM
- August 24th 2010, 10:11 AMArchie Meade