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

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

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

Different Formulae of Derivative: 1. 𝑑(𝑐) 𝑑𝑥 =0 2. . 𝑑(𝑥) 𝑑𝑥 =1 3. 𝑑(𝑥𝑛) 𝑑𝑥 =𝑛𝑥𝑛−1 4. . 𝑑(𝑒𝑥) 𝑑𝑥 =ex 5. . 𝑑(𝑎𝑥) 𝑑𝑥 =𝑎𝑥 lna 6. . 𝑑(𝑥) 𝑑𝑥 = 1 2𝑥 7. . 𝑑(𝑙𝑛𝑥) 𝑑𝑥 = 1 𝑥 8. . 𝑑(𝑙𝑜𝑔𝑎𝑥) 𝑑𝑥 = 1 𝑥 𝑙𝑜𝑔𝑎𝑒

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

GROUP WORK 1.Find the differentiation of the following functions w.r.to x i.sin2x ii. Cos3x iii.Tan5x iv.cot7x v.cosec7x

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

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

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}

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