Differentiation Question 288
Question: If $ y={{\tan }^{-1}}( \frac{\sqrt{x}-x}{1+{x^{3/2}}} ), $ then $ y’(1) $ is
[AMU 2000]
Options:
A) 0
B) $ \frac{1}{2} $
C) - 1
D) $ -\frac{1}{4} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ y={{\tan }^{-1}}( \frac{\sqrt{x}-x}{1+{x^{3/2}}} )={{\tan }^{-1}}(\sqrt{x})-{{\tan }^{-1}}(x) $
Therefore $ {y}’=\frac{1}{1+x}.\frac{1}{2\sqrt{x}}-\frac{1}{1+x^{2}}\Rightarrow {y}’(1)=\frac{1}{2}.\frac{1}{2}-\frac{1}{2}=\frac{-1}{4} $ .
BETA
