Page 277 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes dy y log y
dx y x

dy
Example: Find , if, y a x y y x
dx
Solution:
Taking logs, we get

logy x y loga x logy
Differentiating w.r.t. x
1 dy dy 1 dy
log x 1 x log y 1
y dx dx y dx

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

dy m n
m
Example: Find , if, x y n x y
dx
Solution:

Taking logs, we get
m log x n log y (m n )log x y

Differentiating w.r.t. x

1 1 dy 1 dy
m n (m n ) 1
x y dx x y dx

m n dy m n m n dy
i.e.,
x y dx x y x y dx
dy n m n m n m
dx y x y x y x

dy nx ny my ny mx nx mx my
i.e.,
dx y x y x x y

dy nx my nx my
i.e.,
dx y x y x x y
dy (nx my ) nx my
i.e.,
dx y x y x x y

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