Question

If $y=e^x.\cot x$ then $dy/dx$ will be

• A. $e^x\cot x-cosecx$
• B. $e^x({\cot }^{2}x-cose{c}^{2}x)$
• C. $e^x(\cot x-cose{c}^{2}x)$
• D. $e^x\cot x-cose{c}^{2}x$

Answer 1

The correct option is C $e^x(\cot x-cose{c}^{2}x)$

$y=e^x.cotx\frac{dy}{dx}=e^x\frac{d}{dx}\left(cotx\right)+cotx\frac{d}{dx}\left(e^x\right)=e^x(-cose{c}^{2}x)+cotx\left(e^x\right)=e^x[cotx-cose{c}^{2}x]$