Page 257 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

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

x 2 3x 2 2 x 3 2x 1 0
2
x 2

3x 3 6x 2 2x 4 x 3 2x
2
x 2
2x 3 6x 2 4
x 2 2

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

d d
x 3 x 1 x 2 x 2 x 1 x 1 x 2 1
dx dx
2
x 3
x 3 x 1 1 x 2 1 x 1 x 2
2
x 3
x 3 2x 3 x 1 x 2
2
x 3
2 2
2x 9x 9 x 3x 2
2
x 3
x 2 6x 7
2
x 3

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