AP EAMCET · Maths · Differentiation
The domain of the derivative of the function \(f(x)=\frac{x}{1+|x|}\) is
- A \([0, \infty)\)
- B \((-\infty, 0)\)
- C \((-\infty, \infty)\)
- D \((0, \infty)\)
Answer & Solution
Correct Answer
(C) \((-\infty, \infty)\)
Step-by-step Solution
Detailed explanation
For \(x > 0\), \(f(x) = \frac{x}{1+x}\). \(f'(x) = \frac{1 \cdot (1+x) - x \cdot 1}{(1+x)^2} = \frac{1}{(1+x)^2}\). For \(x \(f'(x) = \frac{1 \cdot (1-x) - x \cdot (-1)}{(1-x)^2} = \frac{1}{(1-x)^2}\).…
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