Differentiation Question 250
Question: The derivative of $ {{\sin }^{-1}}( \frac{2x}{1+x^{2}} ) $ w.r.t. $ {{\cos }^{-1}}( \frac{1-x^{2}}{1+x^{2}} ) $ is
[Karnataka CET 2000; Pb. CET 2004]
Options:
A) -1
B) 1
C) 2
D) 4
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ p={{\sin }^{-1}}\frac{2x}{1+x^{2}}=2{{\tan }^{-1}}x $
and $ q={{\cos }^{-1}}\frac{1-x^{2}}{1+x^{2}}=2{{\tan }^{-1}}x $ ; \ $ \frac{dp}{dq}=\frac{dp/dx}{dq/dx}=1 $ .
BETA
