Differentiation Question 199
Question: Derivative of $ {{\sec }^{-1}}{ \frac{1}{2x^{2}-1} } $ w.r.t $ \sqrt{1+3x} $ at $ x=-\frac{1}{3} $ is
[EAMCET 1991]
Options:
A) 0
B) 1/2
C) 1/3
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{\sec }^{-1}}\frac{1}{(2x^{2}-1)}=2{{\cos }^{-1}}x $
$ \therefore y=2{{\cos }^{-1}}x,\ \ z=\sqrt{1+3x} $
$ \frac{dy}{dz}=\frac{dy}{dx}\div \frac{dz}{dx}=-\frac{2}{\sqrt{1-x^{2}}}.\frac{2\sqrt{1+3x}}{3}=0,( at\ \ \ x=-\frac{1}{3} ) $ .
BETA
