Page 314 - DMTH201_Basic Mathematics-1

Unit 12: Successive Differentiation

Notes
dy dy
(x 2y ) 2 2 ( x ) y 1 2
2
d y dx dx
dx 2 (x 2y ) 2

dy dy
2x 4y x 2y 2x y 4x 2y
dx dx
2
x 2y

dy
3y x 2y 4x 2y
dx
2
x 2y

2x y
3y 3x
x 2y
2
x 2y

y x 2y x 2x y
3 3
x 2y

xy 2y 2 2x 2 xy
3 3
x 2y

2x 2 2xy 2y 2
3
x 2y

x 2 xy y 2
3 2 3
x 2y
6a 2
2
3 ( x 2 xy y 2 a )
x 2y
2
d y
3
Example: Find 2 , if, x y 2 a 5
dn
Solution:
Differentiating w.r.t. x, we get
dy
x 3 2y y 2 3x 2 0
dx
2
dy 3x y 2 3y
3
dx 2x y 2x

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