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)`
`rArry=1/2log_(e)(logx)(thereforelog_(a^(n))(x)=1/nlog_(a)x)`
On differentiating both sides w.r.t.x, we get
`(dy)/(dx)=1/21/(logx)d/(dx)(logx)`
`=1/(log^(2))dot1/x=1/(xlogx^(2))`