Derivative help

Quote:

Originally Posted by gabet16941

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)

1)Product Rule:

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

2)Chain rule:

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

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

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

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