Question

please solve this question friends
Q20

Answer 1

(1/x)×(sec^2x)
option one is correct.

Answer 2

Final Answer : 2cosec2x

Steps:
1)
$y = log( \tan(x) ) \\ = > \frac{dy}{dx} = \frac{1}{tanx} \times \frac{d( \tan(x)) }{dx} \\ \: \: \: \: \: \: \: \: \: = \frac{1}{ \tan(x) } \times { (\sec(x)) }^{2} \\ = \frac{ \cos(x) }{ \sin(x) } \times \frac{1}{ \cos(x) } \times \frac{1}{ \cos(x) } \\ = \frac{2}{2 \sin(x) \cos(x) } \\ = \frac{2}{ \sin(2x) } \\ = 2 \csc(2x)$