# Lecture 7 Limits and Derivatives Class 11

Stop chasing the money and start chasing the passion. Tony Hsieh

# 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). $x \sin x$