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Differentiate $\int_{\sin x}^{\ln x} e^{\tan t}dt$

Differentiate the function $$f(x)=\int_{\sin x}^{\ln x} e^{\tan t}dt.$$

Calculus Integrals
Ava Smith Ava Smith
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\[f'(x)=(\ln x)' e^{\tan (\ln x)}-(\sin x)' e^{\tan (\sin x)}\]
\[=\frac{1}{x}e^{\tan (\ln x)}-\cos x e^{\tan (\sin x)}.\]

Nirenberg Nirenberg
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