1. WELCOME TO THE HIGHER MATHEMATICS CLASS
SHIPAN CHANDRA DEBNATH ASSISTANT PROFESSOR & HEAD OF THE DEPARTMENT DEPARTMENT OF MATHEMATICS CHITTAGONG CANTONMENT PUBLIC COLLEGE

2. DIFFERENTIATION Today`s Topics is Chapter - 9 Exercise -9(D)
Book: Higher Mathematics
Axorpotra Publications

3. Learning Outcomes After complete this chapter students can
Explain Different Formula of Differentiation
Derivative of Different function

4. Different Formulae of Derivative:
1. 𝑑(𝑠𝑖𝑛−1𝑥) 𝑑𝑥 = 1 1−𝑥 𝑑(𝑐𝑜𝑠−1𝑥) 𝑑𝑥 = −1 1−𝑥2
3. 𝑑(𝑡𝑎𝑛−1𝑥) 𝑑𝑥 = 1 1+𝑥 𝑑(𝑐𝑜𝑡−1𝑥) 𝑑𝑥 = −1 1+𝑥2
5. 𝑑(𝑠𝑒𝑐−1𝑥) 𝑑𝑥 = 1 𝑥 𝑥2− 𝑑(𝑐𝑜𝑠𝑒𝑐−1𝑥) 𝑑𝑥 = −1 𝑥 𝑥2−1

5. 9. . 𝑑(𝑠𝑖𝑛𝑥) 𝑑𝑥 =𝑐𝑜𝑠𝑥
10. 𝑑(𝑐𝑜𝑠𝑥) 𝑑𝑥 =−𝑠𝑖𝑛𝑥
11. . 𝑑(𝑡𝑎𝑛𝑥) 𝑑𝑥 =𝑠𝑒𝑐2𝑥
12. . 𝑑(𝑐𝑜𝑡𝑥) 𝑑𝑥 =−cosec2x
13. . 𝑑(𝑠𝑒𝑐𝑥) 𝑑𝑥 =secxtanx
14.. 𝑑(𝑐𝑜𝑠𝑒𝑐𝑥) 𝑑𝑥 =−𝑐𝑜𝑠𝑒𝑐𝑥𝑐𝑜𝑡𝑥

6. GROUP WORK
1.Find the differentiation of the following functions w.r.to x
i.ln{x- (𝑥2 -1)}
ii. ln{ (𝑥 -2)+ (𝑥 +1)}
iii. ln{ ( 1−𝑐𝑜𝑠𝑥 1+𝑐𝑜𝑠𝑥 )}
iv.xx
v.x 1 𝑥

7. vi. (cotx)tanx
vii.

8. EVALUATION
Tell me the First Principle of Derivative
why the derivative of constant is 0?

9. HOME WORK
1.Find the differentiation of the following functions w.r.to x
1.(x) x 3

10. THANKS TO ALL,
DEAR STUDENT
Sir Issac Newton, Father of Calculus