Differentiation Question 101
Question: If $ f(x)=x{{\tan }^{-1}}x $ , then $ f’(1) $ =
[IIT 1979]
Options:
A) $ 1+\frac{\pi }{4} $
B) $ \frac{1}{2}+\frac{\pi }{4} $
C) $ \frac{1}{2}-\frac{\pi }{4} $
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)=x{{\tan }^{-1}}x $
Differentiating w.r.t x, we get $ f’(x)=x\frac{1}{1+x^{2}}+{{\tan }^{-1}}x $
Now put $ x=1 $ , then $ f’(1)=\frac{1}{2}+{{\tan }^{-1}}(1)=\frac{\pi }{4}+\frac{1}{2} $ .
BETA
