Math Differentiability and derivative Differentiability

# Differentiability

The differentiability describes if and where you can differentiate a function.

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### Remember

If the differential quotient exists for a point, the function is differentiable at that point.

A function is differentiable, if every point of the function is differentiable. A differentiable function can not have a non-differentiable point.
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### Hint

If $g(x)$ and $h(x)$ are differentiable, then the functions:
• $f(x)=g(x)\pm h(x)$
• $f(x)=g(x)\cdot h(x)$
• $f(x)=\frac{g(x)}{h(x)}$ ($h(x)\neq0$)
• $f(x)=g(h(x))$
are also differentiable.