Page 267 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
dy
Example: Find , if, x 2 y 2 a 2
dx
Solution: Differentiate w.r.t. x
dy
2x 2y 0
dx
dy
2y 2x
dx
dy 2x
dx 2y

dy x
dx y

dy
Example: Find , if, x 2 y 2 2x 4y 6 0
dx
Solution: Differentiate w.r.t. x
dy dy
2x 2y 2 4 0
dx dx
Cancelling 2, we get

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

dy
Example: Find , if, e x y e x
dx

Solution: Differentiate w.r.t. x
x y d
e x y e x
dx
dy
i.e.,e x y 1 e x
dx

dy e x 1
1 x y y
dx e e
dy 1 e y
i.e.,
dx e y

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