Page 259 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 2
4x 20x 22
2
2
x 7x 12
dy 2 x
Example: Find , if, y x 1 e log x
dx
Solution:
dy 2 x d 2 d x x d 2
x 1 e log x x 1 log x e e log x x 1
dx dx dx dx

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

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

1
1 ( log x ( ) e x 2x ) (e x x 2 ) 0
x
1 ( log ) x 2

x
e
x
e 1 log x 2x 1 log x x
x
2
1 log x
1
x
e 1 log x x 2 logx
x
x
2
1 log x
dy x 5 4x 2 1
Example: Find , if, y
dx x 3 1
Solution:
d d
( x 3 ) 1 ( x 5 4 x 2 ) 1 ( x 5 4 x 2 ) 1 (x 3 ) 1
dy dx dx
dx (x 3 ) 1 2

(x 3 1 )( 5x 4 8x ) (x 5 4x 2 1 )( 3x 2 )
(x 3 ) 1 2

5x 7 5x 4 8x 4 8x 3x 7 12x 4 3x 2
(x 3 ) 1 2

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