NCERT Class 11 Mathematics Solutions: Chapter 13 – Limits and Derivatives Miscellaneous Exercise Part 9 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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,