Page 268 - DMTH201_Basic Mathematics-1

Unit 9: Differential Calculus

Notes
dy
Example: Find , if, x 2/3 y 2/3 a 2/3
dx
Solution: Differentiate w.r.t. x

2 2 1 2 2 1 dy
x 3 y 3 0
3 3 dx

2
Dividing throughout by , we get
3

1 1 dy
x 3 y 3 0
dx
1 dy 1
y 3 x 3
dx
1
dy x 3
dx 1
y 3
1/3
dy y
i.e.,
dx x

dy
Example: Find , if, y log x log x log x .........to
dx

Solution: y log x log x log x .........to

y log x y

Squaring, we get

y 2 logx y
Differentiate w.r.t. x

dy 1 dy
2y
dx x dx

dy dy 1
2y
dx dx x
dy 1
2y 1
dx x
dy 1
dx x 2y 1

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