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  • Explain solution RD Sharma class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question question 23

Explain solution RD Sharma class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question question 23

Answers (1)

Answer:

                (c)

Hint:

We must know about the rules of finding the derivative.

Given:

                \frac{d}{d x}\left\{x^{n}-a_{1} x^{n-1}+a_{2} x^{n-2}+\ldots .+(-1)^{n} a_{n}\right\} e^{x}=x^{n} e^{x} \\

Explanation:

                \frac{d}{d x}\left\{x^{n}-a_{1} x^{n-1}+a_{2} x^{n-2}+\ldots .+(-1)^{n} a_{n}\right\} e^{x}=x^{n} e^{x} \\

                \frac{d}{d x}\left[x^{n}-a_{1} x^{n-1}+a_{2} x^{n-2}+\ldots .+(-1)^{n} a_{n}\right] e^{x} \\

                \begin{aligned} & &\frac{d}{d x}\left[x^{n}-n x^{n-1}+n(n-1) x^{n-2}+\ldots . .+(-1)^{n} a_{n}\right] e^{x} \end{aligned}

Comparing the coefficients of above two equations,

                a_{1}=n, a_{2}=n(n-1)

Similarly,

                a_{r}=n(n-1)(n-2)(n-3) \ldots(n-r+1) \\

                \begin{aligned} & &a_{r}=\frac{n !}{(n-r) !} \end{aligned}

 

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