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Derivatives / Trig / Logs and Exponentials (8 questions)

QuestionAnswer
Differentiate: $\sin(e^x)$ $e^x \cos(e^x)$
Differentiate $e^{\sin(x)}$ $\cos(x) e^{\sin(x)}$
Differentiate $e^{\cos(x)}$ $-\sin(x) e^{\cos(x)}$
Differentiate $\cos(\ln(x))$ $\frac{-\sin(\ln(x))}{x}$
Differentiate $\ln(\cos(x))$ $-\tan(x)$
Differentiate $\ln(\sin(x))$ $\cot(x)$
Differentiate $\ln(\tan(x))$ $\frac{1}{\sin(x) \cos(x)}$
Differentiate $\frac{\sin(x)}{e^x}$ $\frac{\cos(x) - \sin(x)}{e^x}$