Page 262 - DMTH201_Basic Mathematics-1

Unit 9: Differential Calculus

4. log 2x 2 5x 7 Notes

Solution: Let y log 2x 2 5x 7

dy 1 d 2
2x 5x 7
dx 2x 2 5x 7 dx
1
.( 4x ) 5
2x 2 5x 7
1
5. x log x 5
1
Solution: Let y x log x 5

dy 1 1 1 d
x log x 5 x log x
dx 5 dx
1 4 1
x log x 5 x logx 1
5 x
1 4
x log x 5 1 log x
5

2 x
6. x e 2
2
2 x
Solution: Let y x e
dy x 2 1 d 2 x
( 2)(xe ) . (x e )
dx dx
3
2 x
2 x
2 x e x e e x 2x
x
2 x
2 x e 3 e x 2 2x
6
x
2 x e 3x e x 2 2x
2e 2x x 4 2x 5

x 2 1
7.
x 2 1
x 2 1
Solution: Let y
x 2 1

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

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