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  • Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 56 maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 56 maths textbook solution

Answers (1)

Answer: \frac{-2 \log x \sin (\log x)^{2}}{x}

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

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

Solution:

Let  y=\cos (\log x)^{2}

Differentiate with respect to x

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x}\left[\cos (\log x)^{2}\right] \\\\ &\frac{d y}{d x}=-\sin (\log x)^{2} \cdot \frac{d}{d x}\left[(\log x)^{2}\right] \end{aligned}

\begin{aligned} &\frac{d y}{d x}=-\sin (\log x)^{2} \cdot 2 \log x \frac{d}{d x} \log x \\\\ &\frac{d y}{d x}=-\sin (\log x)^{2} \cdot \frac{2 \log x}{x} \\\\ &\frac{d y}{d x}=\frac{-2 \log x \sin (\log x)^{2}}{x} \end{aligned}

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