Question

differentiate the functions with respect to x=2√cot(x²)

Answer 1

. 2√cot( x²). =2cot½(x²). Hence, d/dx{2cot½(x²)}. =2*1/ 2cot(-½)(x²)*{-cosec²(x²)}*2x. = -2xcosec² ...

Answer 2

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