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

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

Answers (1)

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}}

Solution:

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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