Notes: `f(x) = ln(sinhx)` Find the derivative of the function

Thursday, 26 April 2018

$\displaystyle{f{{\left({x}\right)}}}={\ln{{\left({\sinh{{x}}}\right)}}}$ Find the derivative of the function

Jedidiah Hahn

$\displaystyle{f{{\left({x}\right)}}}={\ln{{\left({\sinh{{\left({x}\right)}}}\right)}}}$

Take note that the derivative formula of natural
logarithm is

$\displaystyle\frac{{d}}{{\left.{d}{x}}}{\left[{\ln{{\left({u}\right)}}}\right]}=\frac{{1}}{{u}}\cdot\frac{{{d}{u}}}{{\left.{d}{x}}}$

Applying this formula, the derivative of the function will be

$\displaystyle{f{'}}{\left({x}\right)}=\frac{{d}}{{\left.{d}{x}}}{\left[{\ln{{\left({\sinh{{\left({x}\right)}}}\right)}}}\right]}$

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