Differentiation of Hyperbolic Functions

Calculus Level 3

$\large \dfrac{d}{dx} \sqrt[4]{\dfrac{1+\tanh x}{1-\tanh x}} = \, ?$

Note: $\tanh$ is a hyperbolic function.

\dfrac{e^x}{2}

\dfrac{\sqrt{e^x}}{2}

\dfrac{1}{2\sqrt{e^x}}

\dfrac{1}{2e^x}

1 solution

Rishabh Jain
Jan 20, 2016

$\small{\color{forestgreen}{Using ~ \tan hx=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}}}$ $\dfrac{d}{dx} \sqrt[4]{\dfrac{1+\tan hx}{1-\tan hx}}=\dfrac{d}{dx} \sqrt[4]{\dfrac{e^x}{e^{-x}}}=\dfrac{d}{dx} e^{\dfrac{x}{2}}$ $\color{goldenrod}{=\dfrac{\sqrt{e^x}}{2}}$

would you please describe the hyperbolic function.I didn't get it.

Tanvir Hasan - 5 years, 4 months ago

...I also learnt it on wiki before posting this solution, you may use wiki for learning Hyperbolic functions better..

Rishabh Jain - 5 years, 4 months ago

Differentiation of Hyperbolic Functions

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