Lecture 7 Limits and Derivatives Class 11

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Lecture - 7 Chapter 13 Limits and Derivatives

Questions form NCERT based on First Principle

NCERT EXERCISE 13.2

Question 4.  Find the derivative of the following functions from first principle:
(i). \( x^3-27\)
(ii). \( (x-1)(x-3)\)
(iii). \( \frac{1}{x^2}\)
(iv). \( \frac{x+1}{x-1} \)

MISCELLANEOUS EXERCISE

Question 1.  Find the derivative of the following functions from first principle:
(i). \( -x \)
(ii). \( (-x)^{-1}\)

(iii). \( \sin(x+1) \)

(iv). \( \cos (x – \frac{\pi}{8})\)

Example 19. Find the derivative of f from the first principle, where f is given by
(i). \( f(x) = \frac{2x+3}{x-2}\)
(ii). \( f(x) = x+\frac{1}{x}\)

Example 20. Find the derivative of f(x) from the first principle, where f(x) is
(i). \( \sin x + \cos x\)
(ii). \(x \sin x\)

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