f(x) = (x) / (1 + |x|)

Show from the definition that f: R -> R is differentiable at 0 and find the value of f'(0)

I have been trying to do it from first principles but keep getting no where.

Any help would be appreciated

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- March 12th 2013, 03:37 PMMatt1993Differentiationf(x) = (x) / (1 + |x|)

Show from the definition that f: R -> R is differentiable at 0 and find the value of f'(0)

I have been trying to do it from first principles but keep getting no where.

Any help would be appreciated

- March 14th 2013, 07:24 PMTheEmptySetRe: Differentiation
Note that

Using the limit definition. Taking the limit from the right gives

Taking the limit from the left