1. Differentiate the following w.r.t. x: 

\frac{e ^x }{\sin x }

Answers (1)

Given function is
f(x)=\frac{e ^x }{\sin x }
We differentiate with the help of Quotient rule
f^{'}(x)=\frac{\frac{d(e^x)}{dx}.\sin x-e^x.\frac{(\sin x)}{dx} }{\sin^2 x }
             =\frac{e^x.\sin x-e^x.\cos }{\sin^2 x } = \frac{e^x(\sin x-\cos x)}{\sin^2x}
Therefore, the answer is \frac{e^x(\sin x-\cos x)}{\sin^2x}

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