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(F)
Book: Higher Mathematics
Axorpotra Publications

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

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 value of y2 &y3 if x=2 where y=5x4-3x3+5x+2
2. If y=px+q/x then show that x 𝑑2𝑦 𝑑𝑥2 +2 𝑑𝑦 𝑑𝑥 =2p
3. If y=x+  1/x then show that 2x 𝑑𝑦 𝑑𝑥 +y=2  x
4. If y=secx then show that y2=y(2y2-1)
5. If y=tanx+secx then show that y2= 𝑐𝑜𝑠𝑥 1−𝑠𝑖𝑛𝑥 2
6. If y=excosx then show that (i) 𝑑2𝑦 𝑑𝑥2 -2 𝑑𝑦 𝑑𝑥 +2y=0
(ii) 𝑑4𝑦 𝑑𝑥4 +4y=0

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

8. HOME WORK
1.Find the differentiation of the following functions w.r.to x
1. If y= 𝑙𝑛𝑥 𝑥 then show that 𝑑2𝑦 𝑑𝑥2 = 2𝑙𝑛𝑥−3 𝑥3
2. If y=(ex+e-x)sinx then show that y4+4y=0
3. If y=sin(sinx) then show that 𝑑2𝑦 𝑑𝑥2 + 𝑑𝑦 𝑑𝑥 tanx+ycos2x=0

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