question_answer

Directions: (21 - 25)

Derivative of \[y\text{ }=\text{ }f\left( x \right)\]w.r.t. x (if exists) is denoted by \[\frac{dy}{dx}\] of \[f'\left( x \right)\]and is called the first order derivative of y.

If we take derivative of again, then we get \[\frac{dy}{dx}\left( \frac{dy}{dx} \right)=\frac{{{d}^{2}}y}{d{{x}^{2}}}\] or \[f''\left( x \right)\] and is called the second order derivative of y. Similarly, \[\frac{d}{dx}\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)\] is denoted and defined as \[\frac{{{d}^{3}}y}{d{{x}^{3}}}\]or \[f'''\left( x \right)\] and is known as third order derivative of y and so on.

Based on the above information, answer the following questions.

If \[y={{\tan }^{-1}}\left( \frac{\log \left( e/{{x}^{2}} \right)}{\log \left( e{{x}^{2}} \right)} \right)+{{\tan }^{-1}}\left( \frac{3+2\log \,x}{1-6\log \,x} \right)\], then \[\frac{{{d}^{2}}y}{d{{s}^{2}}}\]is equal to

A) 2

B) 1

C) 0

D) -1