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Question
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Solution
Let, y = `2 sqrt(cot (x^2))`
y = 2 (cot x2)1/2
On differentiating with respect to x,
`dy/dx = 2 d/dx sqrt (cot(x)^2) = 2* 1/2 {cot (x^2)}^(-1/2)* d/dx cot (x^2)`
= `1/(sqrtcot(x^2))* {-cosec^2(x^2)} d/dx (x^2)`
= `1/sqrt(cot(x^2))* {- cosec^2 (x^2)} (2x)`
= `(-2x cosec^2 (x)^2)/(sqrtcot(x^2))`
= `(-2x)/(sin^2 x^2) xx 1/(cossqrtx^2/sinsqrtx^2)`
= `(-2x)/((sinx^2)sqrt(sinx^2) sqrt(cosx^2)`
= `(-2xsqrt2)/(sinx^2 sqrt(2sinx^2 cosx^2))`
= `(-2sqrt(2x))/(sinx^2 sqrt(sin2x^2))`
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