Question

Find the derivative of cosecx . cotx​

Answer 1

Given function :-

• cosec x . cot x

⠀

To find :-

• Derivative of the given function.

⠀

Solution :-

⠀

$\: \: \: \: \: \: \: \: \star\bf\: \: \: {\dfrac{d}{dx} cosec x . cot x}$

⠀

➲ By using product rule

⠀

$\rm\implies{cosec x \dfrac{d}{dx}\: cot x + cot x \dfrac{d}{dx}cosec x}$

⠀

$\rm\implies{cosec x(-cosec^2 x) + cot(-cosec x . cot x)}$

⠀

$\rm\implies{-cosec^3x - cosec x . cot x}$

⠀

$\rm\implies{-cosec^3x - cosec x (cosec^2x - 1)}$

⠀

$\rm\implies{-cosec^3x - cosec^3x + cosec x}$

⠀

$\bf\implies{-2cosec^3x + cosec x}$

⠀

Hence, the derivative of the given function is -2cosec³x + cosec x.