Limits and Derivatives Lecture 9
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Part - 1

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


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}

Limits and Derivatives Lecture 9
Play Video

Part - 2

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.