If f(x) = log(e^x + e^-x), what is f'(log 2)?

Chain Rule, Log Differentiation & Rate of Change · Question 78 of 130

Question 78

HardOriginal question

If $f(x) = \log(e^{x} + e^{-x})$ , what is $f'\left(\log 2\right)$ ?

0

Correct answerYour answer

\frac{2}{5}

Correct answerYour answer

\frac{3}{5}

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1

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$f'(x) = \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$ .
At $x = \log 2$ , $e^{x} = 2$ and $e^{-x} = \frac{1}{2}$ : $\frac{2 - \frac{1}{2}}{2 + \frac{1}{2}} = \frac{3}{5}$ .

Worth noting

$\frac{2}{5}$ is $\frac{1}{u}$ alone, before multiplying by $u' = e^{x} - e^{-x}$ .

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.