have a few derivatives i cannot figure out any help would be greatly appreciated

1.at(a+t)^4

2.sin(2x+5)

3.ln(x cos x)

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- Jun 29th 2008, 06:26 PMgabet16941Derivative help
have a few derivatives i cannot figure out any help would be greatly appreciated

1.at(a+t)^4

2.sin(2x+5)

3.ln(x cos x) - Jun 29th 2008, 06:40 PMIsomorphism
1)Product Rule:

$\displaystyle (at(a+t)^4)' = a(a+t)^4 + 4at(a+t)^3$

2)Chain rule:

Start with $\displaystyle u = 2x+5 \Rightarrow \frac{du}{dx}= 2$,

$\displaystyle (2\sin(2x+5))' =\frac{d(2\sin u)}{du} \frac{du}{dx}= (2\cos u) . 2 = 4 \cos(2x+5)$

3)Smart question, dont directly differentiate. First use log properties, make the problem easier. Then its the chain rule for the second part.

$\displaystyle (\ln(x \cos x))' = (\ln x + \ln \cos x)' = \frac{1}{x} + \frac1{\cos x}(\cos x)' = \frac{1}{x} - \tan x $