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(F) Book: Higher Mathematics Axorpotra Publications

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

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 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

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. 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

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