Page 276 - DMTH201_Basic Mathematics-1

Unit 10: Logarithmic Differentiation

dy Notes
y log 3
dx
dy x
i.e., 3 log3
dx
to
. .
x
5. Let y x x
y x y
Taking logs, we get

log y y log x
Differentiating w.r.t. x

1 dy 1 dy
y log x
y dx x dx
dy 1 y
log x
dx y x

dy 1 y log x y
dx y x

dy y 2
dx x 1 y logx

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

y log e x log y

i.e., y 1 x log y log e log e 1
e
Differentiating w.r.t. x
dy 1 dy
x log y 1
dx y dx

dy x dy
log y
dx y dx

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

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