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

Doorsteptutor material for IMO is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 420K) ↧

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,