Page 256 - DMTH201_Basic Mathematics-1
P. 256
Unit 9: Differential Calculus
Notes
1
Example: Solve 3
x
d 1 d 3
Solution: 3 x
dx x dx
3 x 3 1 3x 4
1
3 4
x
3
x 4
2
2
Example: Solve (x + 1) (x – 1)
d 2 2 d 4
Solution: x 1 x 1 x 1 (on multiplication)
dx dx
d 4 d
x 1
dx dx
3 3
4x 0 4x
x
Example: Solve e (x – 5)logx
d x
Solution: e x 5 log x
dx
d x d d x
x
e x 5 logx e logx x 5 x 5 logx e
dx dx dx
1 x x
x
e x 5 e log x 1 x 5 log x e
x
5
x
e 1 log x x log x 5log x
x
x 5
e 1 log x x log x 5log x
x
5
x
e 1 4log x x log x
x
e x log x
Solve 2
Task 1 x
dy 2x 1
Example: Find , if, y 2
dx 1 x
Solution:
2 d d 2
1 x 2x 1 2x 1 1 x
dy dx dx
dx 1 x 2 2
1 x 2 2 2x 1 2x
2
2
1 x
LOVELY PROFESSIONAL UNIVERSITY 249