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(C)
Book: Higher Mathematics
Axorpotra Publications

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

4. Different Formulae of Derivative:
1. 𝑑(𝑐) 𝑑𝑥 = 𝑑(𝑥) 𝑑𝑥 =1
3. 𝑑(𝑥𝑛) 𝑑𝑥 =𝑛𝑥𝑛− 𝑑(𝑒𝑥) 𝑑𝑥 =ex
5. . 𝑑(𝑎𝑥) 𝑑𝑥 =𝑎𝑥 lna 𝑑(𝑥) 𝑑𝑥 = 1 2𝑥
7. . 𝑑(𝑙𝑛𝑥) 𝑑𝑥 = 1 𝑥 𝑑(𝑙𝑜𝑔𝑎𝑥) 𝑑𝑥 = 1 𝑥 𝑙𝑜𝑔𝑎𝑒

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.sin2x
ii. Cos3x
iii.Tan5x
iv.cot7x
v.cosec7x

7. vi. (ax2+bx+c)
vii. xsinx
viii. tanex2
ix.ln(sinx2)
x.sin2[ln(secx)]

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
i. sin2[ln(x2)]
ii. e5lntan5x
iii.x0cosx0
iv. 𝑡𝑎𝑛𝑥−𝑐𝑜𝑡𝑥 𝑡𝑎𝑛𝑥+𝑐𝑜𝑡𝑥
v.sinln{cosec7x}

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