The set of points where f(x)=x1+|x| is differentiable is

f(x)=x1+|x|f1(x)=(1+|x|).1−x(|x|x)(1+|x|)2 =1(1+|x|)2f(x) is differentiable ∀x∈R

The set of points where f(x)=x1+|x| is differentiable is

f(x)=x1+|x|f1(x)=(1+|x|).1−x(|x|x)(1+|x|)2 =1(1+|x|)2f(x) is differentiable ∀x∈R

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The set of points where $f (x) = \frac{x}{1 + | x |}$ is differentiable is

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$(- \infty, \infty)$

$(0, \infty)$

$(- \infty, - 1) \cup (- 1, \infty)$

$(- \infty, 0) \cup (0, \infty)$

answer is A.

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Detailed Solution

$f (x) = \frac{x}{1 + | x |}$

$f^{1} (x) = {\frac{(1 + | x |) .1 - x (\frac{| x |}{x})}{{(1 + | x |)}^{2}}}^{} = \frac{1}{{(1 + | x |)}^{2}}$

$f (x)$ is differentiable $\forall x \in R$

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The set of points where f(x)=x1+|x| is differentiable is

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The set of points where $f (x) = \frac{x}{1 + | x |}$ is differentiable is