Page 255 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 2
x x 1
Example: Solve 2
x – x 1
d x 2 x 1
Solution: 2
dx x x 1
d d
x 2 x 1 x 2 x 1 x 2 x 1 x 2 x 1
dx dx
x 2 x 1 2

x 2 x 1 2x 1 x 2 x 1 (2x 1)
x 2 x 1 2

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

2x 2 2 2 x 2 1
x 2 x 1 2 x 2 x 1 2
e x 1
Example: Solve x
e – 1
d x x d x
x
d e x 1 e 1 dx e 1 e 1 dx e 1
Solution: x 2
dx e 1 e x 1

e x 1 e x e x 1 e x
2
x
e 1
e 2x e x e 2x e x
2
x
e 1
2e x
2
x
e 1
e x
Example: Solve 2
1 – x
2 d x x d 2
d e x 1 x dx e e dx 1 x
Solution: 2 2
dx 1 x 1 x 2

1 x 2 e x e x 2x
2
2
1 x
x 2
e 1 x 2x
2
2
1 x

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