NCERT Class 11 Mathematics Solutions: Chapter 13 –Limits and Derivatives Miscellaneous Exercise Part 9

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In figure derivation of elementary functions are shown.

Elementary Functions Derivations

In figure derivation of elementary functions are shown.

1. Find the derivative of the following functions (it is to be understood that are fixed non-zero constants and are integers):

Answer:

By quotient rule,

2. Find the derivative of the following functions (it is to be understood that are fixed non-zero constants and are integers):

Answer:

Accordingly,

[By Leibnitz product rule]

………..eq (1)

[By Leibnitz product rule]

[Using (1)]

Consider

……..eq (2)

Consider,

So, our assertion is true for .

So, by mathematical induction,