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explain solution RD Sharma class 12 chapter Differentiation exercise 10.2 question 55 maths

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Answer: -2 x \tan x^{2}

Hint: you must know the rule of solving derivative of logarithm and trigonometric functions

Given: \log \left(\cos x^{2}\right)


Let  y=\log \left(\cos x^{2}\right)

Differentiate with respect to x

\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{d}{d x}\left\{\log \left(\cos x^{2}\right)\right\}                    \left[\therefore \frac{d}{d x} \log x=\frac{1}{x}\right]

\frac{d y}{d x}=\frac{-2 x \sin x^{2}}{\cos x^{2}}                          [  Using chain rule ]

\frac{d y}{d x}=-2 x \tan x^{2}

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