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need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 11

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Answer: e^{x} \times 3^{e^{x}} \log (3)

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

Given: 3^{e^{x}}


Let  y=3^{e^{x}}

Differentiating with respect to x

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

\frac{d y}{d x}=e^{x} \times 3^{e^{x}} \log (3)


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