d/dx {log3 x x logx 3} =

Question

\(\frac{d}{dx}\{log_3 x \times log _x 3\} = \)

(A) \(\frac{1}{9}\) 

(B) 9

(C) 2 log 3

(D) 0

Answer 1

Correct option is (D) 0

\(f(x) = (\log_3x \times \log_x3)\)

\(= \frac{\ln x}{\ln 3} \times \frac{\ln 3} {\ln x}\)

\(= 1\)

Since f(x) = 1, its derivative is:

\(\frac d{dx}(\log_3x \times \log_x3) = 0\)

Answer 2

Correct option is (D) 0