Page 253 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
Example: Solve x 100

d 100 100 1 99
Solution: x 100x 100x
dx

Example: Solve (2x + 3) 2
d 2 d 2 d 2 d d
x
Solution: 2x 3 4x 12x 9 4 x 12 ( ) (9)
dx dx dx dx dx
4(2 ) 12(1) 0 8x 12
x

Example: Solve (x + 1) 3

d 3 d 3 2
Solution: x 1 x 3x 3x 1
dx dx
d 3 d 2 d d
x 3 (x ) 3 ( ) (1)
x
dx dx dx dx
x
3x 3 1 3(2 ) 3(1) 0
3x 2 6x 3
x 2 – 5x 1
Example: Solve
x
d x 2 5x 1 d x 2 5x 1
Solution:
dx x dx x x x

d 2 1 1 1 1
x 2 5x 2 x 2
dx
d 3 1 1
x 2 5x 2 x 2
dx

d 3 d 1 d 1
(x 2 ) 5 (x 2 ) (x 2 )
dx dx dx
3 3 1 1 1 1 1 1 1
x 2 5 x 2 x 2
2 2 2

3 1 5 1 1 3
x 2 x 2 x 2
2 2 2

Task Differentiate w.r.t.
(1) e 3x (2) log (2x + 3)
e

246 LOVELY PROFESSIONAL UNIVERSITY