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Differentiate $f(x)=\int_{\sin x}^{2} \ln (\cos u) du$

Differentiate the function 

$$f(x)=\int_{\sin x}^{2} \ln (\cos u) du$$

Calculus Integrals Derivatives
Bradz Bradz
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We have 
\[f'(x)= (2)' \ln (\cos 2)-(\sin x)' \ln (\cos (\sin x))=0-\cos x \ln (\cos (\sin x))\]
\[=-\cos x \ln (\cos (\sin x)).\]

Nirenberg Nirenberg
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