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  • Please solve RD Sharma class 12 chapter Differentiation exercise 10.8 question 1 maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.8 question 1 maths textbook solution

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Answer: 2 \sec ^{2}\left(x^{2}\right) \tan \left(x^{2}\right)

Hint:

\begin{aligned} &\text { Let } u=\sec ^{2}\left(x^{2}\right) ; v=x^{2} \\\\ &\frac{d u}{d v}=\frac{\frac{d u}{d x}}{\frac{d v}{d x}} \end{aligned}


Given:  \sec ^{2}\left(x^{2}\right) \text { w.r.t } x^{2}

Explanation:

\begin{aligned} &\text { Let } u=\sec ^{2}\left(x^{2}\right), v=x^{2} \\\\ &\frac{d u}{d x}=2 \sec \left(x^{2}\right)\left[\sec x^{2} \tan x^{2} \times 2 x\right] \end{aligned}

        =4 x \sec ^{2}\left(x^{2}\right) \tan \left(x^{2}\right)                    (chain rule)

\begin{aligned} &\frac{d v}{d x}=2 x \\\\ &\frac{d u}{d v}=\frac{\frac{d u}{d x}}{\frac{d v}{d x}}=\frac{4 x \sec ^{2}\left(x^{2}\right) \tan \left(x^{2}\right)}{2 x} \end{aligned}

       =2 \sec ^{2}\left(x^{2}\right) \tan \left(x^{2}\right)

 

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