How do you know if a function is differentiable

One of the most important skills that students need to learn is How do you know if a function is differentiable.

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The rules of differentiation tell us that the derivative of \(x^3\) is \(3x^2\), the derivative of \(x^2\) is \(2x\), and the derivative So, the derivative of \(f\) is \(f'(x) = 3x^2 + 6x + 2\). This derivative exists for every possible value of \(x\)! we can
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Differentiable function

Presumably, you have been given a function defined piecewise over an interval, and you want to know whether the function is differentiable at the edges where the pieces meet. Suppose the

How to determine whether this function is differentiable at a

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Differentiability and continuity (video)

If the function is undefined or does not exist at a point, then we say that the function is discontinuous. Definition of Differentiability : f ( x) is said to be differentiable at the point x = a
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Continuity and Differentiability (Fully Explained w/ Examples!)

The function is differentiable from the left and right. As in the case of the existence of limits of a function at x 0, it follows that exists if and only if both exist and f' (x 0 -) = f' (x 0 +) Hence if and only if f' (x 0 -) = f' (x 0 +) . If any one

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The function f is differentiable at x if lim

What is Differentiable? A function is said to be differentiable if the derivative of the function exists at all points in its domain. Particularly, if a function f (x) is differentiable at x = a, then f′ (a) exists in the domain. Let us look at some