Page 275 - DMTH201_Basic Mathematics-1
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Basic Mathematics – I
Notes x
2. Let y x x
Taking logs, we get
log y x x log x
Taking logs again, we get
log logy x logx log logx
Differentiate w.r.t. x
1 1 dy 1 1 1
x log x 1
log y y dx x log x x
dy 1
y log y 1 log x
dx x log x
dy x x x 1
i.e., x x log x 1 log x
dx x log x
3. Let y x x x
2
x
y x
Taking logs, we get
log y x 2 log x
Differentiate w.r.t. x
1 dy 2 1
x log x 2x
y dx x
dy
y x 2 logx
x
dx
dy x x
x
i.e., x x 2 log x
dx
4. Let y 3 x
Taking logs, we get
log y x log 3
Differentiating w.r.t. x
1 dy
log 3 1
y dx
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