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provide solution for RD Sharma maths class 12 chapter Differentiation exercise  10.2 question 10

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Answer: 3 x^{2} \times 2^{x^{3}} \times \log _{e} 2

Hint: You must know the rules of solving derivative of polynomial function.

Given: 2^{x^{8}}


Let  y=2^{x^{3}}

Differentiating with respect to x         

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x}\left(2^{x^{3}}\right) \\ &\frac{d y}{d x}=2^{x^{3}} \times \log _{e} 2 \frac{d}{d x}\left(x^{3}\right) \end{aligned}                        \frac{d}{d x} a^{x}=a^{x} \log a        [using chain rule]

\frac{d y}{d x}=3 x^{2} \times 2^{x^{3}} \times \log _{e} 2

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