Page 311 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 2 2
6x 6xy 6y
(x 2y ) 3

x 2 xy y 2 6 0
6 3 3 0
x 2y x 2y

2
d y
0
dx 2
2
d y ax b
Example: Find 2 , if y
dx bx a
ax b
Solution: y
bx a
dy bx a a ax b b
dx bx a 2

abx a 2 abx b 2
2
bx a
a 2 b 2
bx a 2

2
d y 2 2 2 1 d
a b 2 bx a bx a
dx 2 dx
2b b 2 a 2
3
2 b 2 a 2 bx a b 3
bx a
2
d y
x
Example: Find , if y a .
dx 2
Solution: y = a x
dy
a x log a
dx
2
d y x 2
a log a
dx 2
m
2
Example: If y x x 2 1 , prove that x 2 1 y 2 xy 1 m y 0 .
m
Solution: y x x 2 1

m 1 d
y 1 m x x 2 1 x x 2 1
dx

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