Key to "Find the first and second derivatives of the..."

CoormaBak9

Answered question

2021-10-07

Find the first and second derivatives of the function.
$f (x) = \ln (x + 4)$
$f^{'} (x) =$
$f^{″} (x) =$

Arham Warner

Skilled2021-10-08Added 102 answers

Formula Used

\frac{d}{d x} (\ln x) = \frac{1}{x}

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x^{2}}

We have,

f (x) = \ln (x + 4)

Differentiating both sides w.r.t x we obtain,

f^{'} (x) = \frac{d}{d x} (\ln (x + 4))

f^{'} (x) = \frac{1}{x + 4}

Again differentiating the above equation w.r.t x both sides we get,

f^{″} (x) = \frac{d}{d x} (\frac{1}{x + 4})

= - \frac{1}{{(x + 4)}^{2}}

Jeffrey Jordon

Expert2022-08-14Added 2605 answers

Answer is given below (on video)

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