TS EAMCET · Maths · Differentiation
If \(f(x)=\frac{x}{1+|x|}\), for \(x \in R\), then \(f^{\prime}(0)\) is equal to :
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
We have, \(f(x)=\frac{x}{1+|x|}\) \(f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{f(0+h)-f(0)}{h}\) \(=\lim _{h \rightarrow 0} \frac{\frac{h}{1+|h|}-0}{h}\) \(=\lim _{h \rightarrow 0} \frac{1}{1+|h|}=1\)
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