Differentiability

Differentiability Examples

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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) = \(\displaystyle{\lim_{h \to 0}}\) \(f(x+h) – f(x)\over h\) = […]

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Differentiability of a Function – Differentiable vs Continuous

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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

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