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