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  • Provide Solution for RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question Question 11

Provide Solution for RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question Question 11

Answers (1)

Answer:

                (a)

Hint:

We know about the derivative of polynomials.

Given:

               f\left ( x \right )   be a polynomial, f\left ( e \right )^{x} .

Explanation:

                  y=f\left ( e \right )^{x}

                \begin{gathered} \frac{d}{d x}\left(f\left(e^{x}\right)\right)=f^{\prime}\left(e^{x}\right) \times \frac{d}{d x}\left(e^{x}\right) \\ \end{gathered}

                 =f^{\prime}\left(e^{x}\right) \cdot e^{x}

Similarly,

                \begin{aligned} & \frac{d^{2}}{d x^{2}}\left(f\left(e^{x}\right)\right)=f "\left(e^{x}\right) \frac{d}{d x}\left(e^{x}\right) e^{x}+\frac{d}{d x}\left(e^{x}\right) f^{\prime}\left(e^{x}\right) \\ \end{aligned}

                \Rightarrow \quad f^{\prime \prime}\left(e^{x}\right) e^{2 x}+f^{\prime}\left(e^{x}\right)\left(e^{x}\right)

 

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