# Help with differentiation.

• Jul 12th 2010, 08:41 AM
blue19
Help with differentiation.
dy/dx of :

y=cos(x) / (e^x) +1

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This is what I have got so far:

Use the quotient rule, so make u=cos(x) and make v=(e^x)+1

y=u/v

dy/dx = [(e^x)+1 * -sin(x) - cos(x) * e^x ] / ((e^x)+1)^2

What do I do next?
• Jul 12th 2010, 09:03 AM
Chris11
looks like you got it. :)
• Jul 12th 2010, 09:21 AM
Ackbeet
Use some more parentheses, though! Parentheses make things clearer.
• Jul 12th 2010, 09:25 AM
chaoticmindsnsync
a different approach
You did the quotient rule just fine, but I often avoid it if I'm not required to use it. Any quotient rule problem I've ever encountered can become a product rule + chain rule problem. Consider the following:

$\displaystyle y=\frac{\cos(x)}{e^x+1}=\cos(x)(e^x+1)^{-1}$

Then,

$\displaystyle \frac{dy}{dx}=-\sin(x)(e^x+1)^{-1}+\cos(x)(-1)(e^x+1)^{-2}(e^x)$

$\displaystyle =(e^x+1)^{-2}[(e^x+1)(-\sin(x))-(e^x)(\cos(x))]$

$\displaystyle =\frac{(e^x+1)(-\sin(x))-(e^x)(\cos(x))}{(e^x+1)^2}$

Much easier in my opinion, and you get the same answer.