# Differentiability

## Differentiability Examples

Here you will learn some differentiability examples for better understanding of differentiability concepts. Example 1 : If f(x + y) = f(x) + f(y) – 2xy – 1 for all x and y. If f'(0) exists and f'(0) = -sin$$\alpha$$, then find f{f'(0)}. Solution : f'(x) = $$\displaystyle{\lim_{h \to 0}}$$ $$f(x+h) – f(x)\over h$$ = …

## Differentiability of a Function – Differentiable vs Continuous

Here, you will learn differentiability of a function and differentiability at a point and over an Interval. Let’s begin – Meaning of Derivative The instantaneous rate of change of a function with respect to the dependent variable is called derivative. Let ‘f’ be a given function of one variable and let $$\Delta$$x denote a number …