question_answer

Directions: (6 - 10)

Let \[f\left( x \right)\text{ }=\text{ }f\left( t \right)\] and \[y=g\left( t \right)\] be parametric forms with t as a parameter, then \[\frac{dy}{dx}=\frac{dy}{dt}\times \frac{dt}{dx}=\frac{g'\left( t \right)}{f'\left( t \right)}\], where \[f'\left( t \right)\ne 0\].

On the basis of above information, answer the following questions.

The derivative of \[f\left( \tan \,x \right)\]w.r.t. \[g\left( sec\text{ }x \right)\]at \[x=\frac{\pi }{4}\], where \[f'\left( 1 \right)=2\] and \[g'\left( \sqrt{2} \right)=4\], is

A) \[\frac{1}{\sqrt{2}}\]

B) \[\sqrt{2}\]

C) 1

D) 0