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TS EAMCET · Maths · Differentiation

If \(f(x)=\frac{x}{1+|x|}\), for \(x \in R\), then \(f^{\prime}(0)\) is equal to :

  1. A 0
  2. B 1
  3. C 2
  4. D 3
Verified Solution

Answer & Solution

Correct Answer

(B) 1

Step-by-step Solution

Detailed explanation

We have, \(f(x)=\frac{x}{1+|x|}\) \(f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{f(0+h)-f(0)}{h}\) \(=\lim _{h \rightarrow 0} \frac{\frac{h}{1+|h|}-0}{h}\) \(=\lim _{h \rightarrow 0} \frac{1}{1+|h|}=1\)