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Math Help - Derivative help

  1. #1
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    Derivative 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)
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  2. #2
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    Quote Originally Posted by gabet16941 View Post
    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
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