am trying to differentiate these equations

$\displaystyle y = tan^2(x)^3 + cos 2x$ and

$\displaystyle y=(e^x)^2/ln(2x)$

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- Apr 9th 2010, 01:43 PMsigma1Differenciation
am trying to differentiate these equations

$\displaystyle y = tan^2(x)^3 + cos 2x$ and

$\displaystyle y=(e^x)^2/ln(2x)$ - Apr 9th 2010, 01:55 PMcgiulz
- Apr 9th 2010, 02:05 PMsigma1
i know that but am having a bit of problem separating the variable that is making something "U" . i would like to see how it is done if that is not too much of a trouble. am trying to catch up quickly on calculus.

- Apr 9th 2010, 02:32 PMmacosxnerd101
U substitution is a topic for integration, not differentiation. If you can show us your work, we will be more than happy to help point you in the right direction.

You may also want to check out this link, which covers product, quotient and chain rules for differentiation: Product Rule, Quotient Rule, and Chain Rule Tutorial - Apr 9th 2010, 03:28 PMtom@ballooncalculus
Just in case a picture helps...

http://www.ballooncalculus.org/asy/diffChain/quot3.png

... where

http://www.ballooncalculus.org/asy/chain.png

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).

__Spoiler__:

________________________________________

Don't integrate - balloontegrate!

Balloon Calculus: Standard Integrals, Derivatives and Methods

Balloon Calculus Drawing with LaTeX and Asymptote! - Apr 9th 2010, 03:41 PMharish21
1. the derivative of $\displaystyle tan^{2}(x)^3 = 2tan(x^3)sec^2(x^3) 3x^2$

Likewise find out the derivaitve of $\displaystyle cos2x$ and add them up

2. try the quotient rule, show how much effort you put on this problem. Post if you have any errors and they will be fixed. - Apr 9th 2010, 05:07 PMAllanCuz
I'll help you a bit with the first one to get you started

$\displaystyle y = tan^2(x)^3 + cos 2x$

Now let $\displaystyle p = tan^2(x)^3, q = cos2x$

We want Y` so

$\displaystyle y` = p` + q`$

This makes it easy, all we need to do is differentiate P and Q seperately and then add them up!

Well Q` is fairly easy

$\displaystyle q` = -2sin2x $

I leave $\displaystyle tan^2(x)^3$ to you. But I would like to let you know that

$\displaystyle Tan^2x = Sin^2x/Cos^2x $

This might make it easiar to apply quotient rule? - Apr 9th 2010, 05:18 PMmr fantastic
- Apr 9th 2010, 05:23 PMAllanCuz
- Apr 9th 2010, 07:04 PMsigma1
thanks alot guys i did it and i seem to get the answer by letting

http://www.mathhelpforum.com/math-he...dc13e1a3-1.gif then http://www.mathhelpforum.com/math-he...58737ed0-1.gif

to get du/dx of http://www.mathhelpforum.com/math-he...7741411d-1.gif i had to apply the chain rule again

now i dIfrenciated http://www.mathhelpforum.com/math-he...e511bc5e-1.gif and i gothttp://www.mathhelpforum.com/math-he...10d42a0f-1.gif is that correct - Apr 9th 2010, 09:16 PMharish21