# Class 11 Lecture 9 Limits and Derivatives

Patience, persistence, and perspiration make an unbeatable combination for success. – Napoleon Hill

# Lecture - 9 Chapter 13 Limits and Derivatives

All rules for direct differentiation Detailed Explanation and Tricks for direct derivative in case of, Addition and Subtraction, Multiplication (Product Rule)

 NCERT EXERCISE 13.2

Question 11.  Find the derivative of the following functions:
(i). $$\sin x \cos x$$
(ii). $$\sec x$$
(iii). $$5 \sec x + 4 \cos x$$
(iv). $$\cosec x$$
(v). $$3 \cot x + 5 \cosec x$$
(vi). $$5 \sin x – 6 \cos x + 7$$
(vii). $$2 \tan x – 7 \sec x$$

Question 9. Find the derivative of
(i). $$2x – \frac{3}{4}$$
(ii). $$(5x^3+3x-1)(x-1)$$
(iii). $$x^{-3}(5+3x)$$
(iv). $$x^5 (3-6x^{-9})$$
(v). $$x^{-4}(3-4x^{-5})$$
(vi). $$\frac{2}{x+1}-\frac{x^2}{3x-1}$$

##### Clip - 1

Division (Quotient Rule)

Question 8. Find the derivative of $$\frac{x^n-a^n}{x-1}$$ for some constant a.

Question 7.  For some constants a and b, find the derivative of
(i). $$(x-a)(x-b)$$
(ii). $$(ax^2+b)^2$$
(iii). $$\frac{x-a}{x-b}$$

Question 6.  Find the derivative of $$x^n+ax^{n-1}+a^2x^{n-2}+ \dots + a^{n-1}x+a^n$$ for some fixed real number a.

Question 5.  For the function $$f(x) = \frac{x^{100}}{100}+\frac{x^{99}}{99}+ \dots + \frac{x^2}{2}+x+1$$

Prove that $$f'(1)=100f'(0)$$.

Question 1. Find the derivative of $$x^2-2$$ at $$x= 10$$.

Question 2. Find the derivative of $$x$$ at $$x= 1$$.

Question 3. Find the derivative of $$99x$$ at $$x= 100$$.