Question

differentiate the function 2√cot (x^5) w.r.t x​

Answer 1

$let \: \: \: \: \: y = 2 \sqrt{cot {x}^{5} } \\ \\ \frac{dy}{dx} = 2 \frac{1}{2 \sqrt{cot {x}^{5} } } \frac{d}{dx} cot {x}^{5} \\ \\ \frac{dy}{dx} = \frac{1}{ \sqrt{cot {x}^{5} } } ( - {cosec}^{2} {x}^{5} ) \frac{d}{dx} {x}^{5} \\ \\ \frac{dy}{dx} = \frac{ - {cosec}^{2} {x}^{5} }{ \sqrt{cot {x}^{5} } } 5 {x}^{4} \\ \\ \frac{dy}{dx} = \frac{ - 5 {x}^{4}. {cosec}^{2} {x}^{5} }{ \sqrt{cot {x}^{5} } }$