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Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 13 maths textbook solution

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Answer: (2 x+2) 3^{x^{2}+2 x} \log _{e} 3

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

Given: 3^{x^{2}+2 x}


Let  y=3^{x^{2}+2 x}

Differentiating with respect to x

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

\frac{d y}{d x}=(2 x+2) 3^{x^{2}+2 x} \log _{e} 3

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