Question

If $y=e^x\cot \left(x\right)$, then $\frac{dy}{dx}$ will be

• A. $e^x\cot \left(x\right)-{\csc }^2\left(x\right)$
• B. $e^x{\csc }^2\left(x\right)$
• C. $e^x\left(\cot \left(x\right)-{\csc }^2\left(x\right)\right)$
• D. $e^x\cot \left(x\right)$

Answer 1

The correct option is C $e^x\left(\cot \left(x\right)-{\csc }^2\left(x\right)\right)$

$y=e^x\cot \left(x\right)$
$\frac{dy}{dx}=e^x\frac{d}{dx}\cot \left(x\right)+\cot \left(x\right)\frac{d}{dx}{e}^x$
$=e^x\left(\cot \left(x\right)-{\csc }^2\left(x\right)\right)$