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# 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}

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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.