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jeliceg2

Answered question

2021-11-21

Compute the derivative.

g (x) = {\tan h}^{- 1} (e^{x})

Answer & Explanation

Mespirst

Beginner2021-11-22Added 17 answers

We have to compute the derivative of the function:

g (x) = {\tan h}^{- 1} (e^{x})

We know the formula of derivatives,

\frac{d e^{x}}{d x} = e^{x}

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

\frac{d g (x)}{d x} = g^{'} (x)

Finding derivative of the function with respect to 'x' by applying above formula, we get

\frac{d g (x)}{d x} = \frac{d {\tan h}^{- 1} (e^{x})}{d x}

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

= \frac{1}{1 - e^{2 x}} \times e^{x}

= \frac{e^{x}}{1 - e^{2 x}}

Hence, derivative of the function is

= \frac{e^{x}}{1 - e^{2 x}}

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