Question

Derivative of log_e² (logx) with respect to x is _______.

Options

• `2/(x log x)`

• `1/(x log x)`

• `1/(x log x^2)`

• `2/(log x)`

Answer 1

Derivative of log_e² (logx) with respect to x is `underline(1/(x log x^2))`.

Explanation:

Let y = log_ex  (log x)

`=> "y" = 1/2 log_"e" (log x)  (because log_("a"^"n")n (x) = 1/"n" log_"a" x)`

On differentiating both sides w.r.t. x, we get

`"dy"/"dx" = 1/2 1/(log x) "d"/"dx" (log x)`

`= 1/(log x^2) * 1/x = 1/(x log x^2)`