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Find the derivative of f(x)\, with respect to x\,: f(x)=\ln(\sin(e^{x}))\,

Here, we must use the chain rule inside of the chain rule.

f'(x)={\frac  {1}{\sin(e^{x})}}{\frac  {d}{dx}}\sin e^{x}={\frac  {1}{\sin(e^{x})}}\cos(e^{x}){\frac  {d}{dx}}e^{x}={\frac  {1}{\sin(e^{x})}}\cos(e^{x})(e^{x})\,

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