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

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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,