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Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  22

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Answer: the correct answer is \frac{3 x^{2}}{1+x^{6}}

Hint: integrate the function.

Given: \frac{d}{\mathrm{dx}} f(x)=\frac{1}{1+x^{2}}

Solution: integrating we get

\begin{aligned} &\int \frac{d}{d x}(f(x)) d x=\int\left[\frac{1}{1+x^{2}}\right] d x \\\\ &f(x)=\tan ^{-1} x+e \end{aligned}

\begin{aligned} &f\left(x^{3}\right)=\tan ^{-1}\left(x^{3}\right)+c \\\\ &f^{1}\left(x^{3}\right)=\frac{3 x^{2}}{1+x^{6}} \end{aligned}

So the answer is  \frac{3 x^{2}}{1+x^{6}}


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