Page 258 - DMTH201_Basic Mathematics-1

Unit 9: Differential Calculus

Notes
dy x 1
Example: Find , if, y
dx x 1
Solution:
d d
x 1 x 1 x 1 x 1
dy dx dx
dx x 1 2

x 1 1 0 x 1 1 0
2
x 1
x 1 x 1
2
x 1
2
2
x 1
dy 2 x
Example: Find , if, y x 1 e
dx
Solution:

dy 2 d x x d 2
x 1 e e x 1
dx dx dx
x 2 1 e x e x 2x

e x x 2 1 2x

e x x 1 2

dy x 1 x 2
Example: Find , if, y
dx x 3 x 4
Solution:
2
x 3x dy 2
x 2 7x dx 12
d d
dy x 2 7x 12 x 2 3x 2 x 2 3x 2 x 2 7x 12
dx dx
dx 2
x 2 7x 12

x 2 7x 12 2x 3 x 2 3x 2 2x 7
2
2
x 7x 12
2x 3 14x 2 24x 3x 2 21x 36 2x 3 6x 2 4x 7x 2 21x 14
2
2
x 7x 12
3 2 2
2x 6x 4x 7x 21x 14
2
x 2 7x 12

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