Question

Find the derivative of $\frac{e^x}{\sin x}$.

• A. $e^x\text{cosec}x[\cot x+1]$
• B. $e^x\text{cosec}x[1-\cot x]$
• C. $e^x\sec x[\cot x+1]$
• D. $e^x\sec x[\cot x-1]$

Answer 1

Answer: (B)

$e^x\text{cosec}x[1-\cot x]$

On Differentiation we get

$\frac{d}{dx}{e}^{x}cosecx=-e^x.cosecx\cot x+e^x.cosecx=e^x.cosecx[1-\cot x]$