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(D) Book: Higher Mathematics Axorpotra Publications

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

Different Formulae of Derivative: 1. 𝑑(𝑠𝑖𝑛−1𝑥) 𝑑𝑥 = 1 1−𝑥2 2. . 𝑑(𝑐𝑜𝑠−1𝑥) 𝑑𝑥 = −1 1−𝑥2 3. 𝑑(𝑡𝑎𝑛−1𝑥) 𝑑𝑥 = 1 1+𝑥2 4. 𝑑(𝑐𝑜𝑡−1𝑥) 𝑑𝑥 = −1 1+𝑥2 5. 𝑑(𝑠𝑒𝑐−1𝑥) 𝑑𝑥 = 1 𝑥 𝑥2−1 6. . 𝑑(𝑐𝑜𝑠𝑒𝑐−1𝑥) 𝑑𝑥 = −1 𝑥 𝑥2−1

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.ln{x- (𝑥2 -1)} ii. ln{ (𝑥 -2)+ (𝑥 +1)} iii. ln{ ( 1−𝑐𝑜𝑠𝑥 1+𝑐𝑜𝑠𝑥 )} iv.xx v.x 1 𝑥

vi. (cotx)tanx vii.

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 1.(x) x 2. 3

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