Page 309 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 2. Let y ax 2 bx c
dy
2ax b 0
dx

2
d y
2a 0
dx 2
= 2a
d 3 y
0
dx 3
d 4 y
0
dx 4
ax b
3. Let y
cx d
dy cx d a ax b c
dx cx d 2

acx ad acx bc
cx d 2
ad bc
cx d 2

2
d y ac bc 2c
dx 2 cx d 3

2
d y 2c bc ad
dx 2 cx d 3

d 3 y 6c 2 (bc ad )
dx 3 (cx ) d 4

d 4 y 24c 3 (bc ad )
dx 4 (cx ) d 5
4. Let y = x log x

dy 1
x log x 1 log x
dx x
2
d y 1 1
0
dx 2 x x
d 3 y 1
dx 3 x 2

d 4 y 2
dx 4 x 3

302 LOVELY PROFESSIONAL UNIVERSITY