Derivative of `log_(e^(2))(logx)` with respect to x is . . .

Options

A. `(2)/(xlogx)`
B. `(1)/(xlogx)`
C. `(1)/(xlogx^(2))`
D. `(2)/(logx)`

Answer

C

Explanation

Let `y=log_(e^(2))(logx)`
`impliesy=(1)/(2)log_(e)(logx)" "(becauselog_(a^(n))(x)=(1)/(n)log_(a)x)`
On differentiating both sides w.r.t x, we get
`(dy)/(dx)=(1)/(2)(1)/(logx)(d)/(dx)(logx)`
`=(1)/(logx^(2))*(1)/(x)=(1)/(xlogx^(2))`