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Question

Differentiate the following functions with respect to x

2cot(x2)


Solution

Let y = 2cot(x2)

Differentiate both sides w.r.t. X,

dydx=ddx2(cont x2)1/2=2.12{cot(x2)}121ddxcot (x2)

    [Using chain rule ddxf(g(x))=f(x)ddxg(x)]

= 1cot(x2)[cosec2x2]ddx(x2)

= cosec2(x2)2xcot(x2)=2x cosec2(x2)cot(x2)


Mathematics

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