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Differentiability

If f(x)= |x -...

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If f(x)= \vert x - 2020\vert,then derivative of f(x) at x = 2019

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f (x) = x . | x |

, then its derivative is:

f (x) = {\begin{matrix} \frac{x}{1 + e^{1 / x}} & x \neq 0 0 & x = 0 \end{matrix}

then the left derivative of

f (x)

x = 0

f (x)

has a derivative at

x = a

{lim}_{x \to a} \frac{x f (a) - a f (x)}{x - a}

f (x) = {\begin{matrix} 1, x < 0 1 + s i n x, 0 \leq x < / π_{2} \end{matrix}

, then derivative of f(x) at

x = 0

f (x) = x^{2}

x \leq α, f (x) = a x + b

x > α

f (x)

x = α

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