If I have a piecewise function, must I prove it is continous to show it is differentiable at a point? Or is it if I am able to apply the derivative rules to the function, it must be continous and therefore …

Sep 8, 2025 · Differentiability is a property of a function that tells us whether it has a well-defined tangent line (or slope) at a given point. A function f (x) is said to be differentiable at a point x = …

Feb 1, 2024 · A simple guide: How to know if a function is differentiable. Exploring the criteria and considerations for determining the differentiability of mathematical expressions.

A function is differentiable if the derivative exists at all points for which it is defined, but what does this actually mean? Learn about it here.

In this article, we will explore the meaning of differentiable, how to use differentiability rules to find if the function is differentiable, understand the importance of limits in differentiability, and …

We'll learn how to check if a function is differentiable using easy rules, understand why limits are important in this idea, and discover some interesting facts about it.

To be differentiable at a certain point, the function must first of all be defined there! As we head towards x = 0 the function moves up and down faster and faster, so we cannot find any value it …

Nov 16, 2022 · In this section we’re going to prove many of the various derivative facts, formulas and/or properties that we encountered in the early part of the Derivatives chapter. Not all of …

1 day ago · This page covers the derivative as a function, detailing its definition via the difference quotient and various notations. It explains how to calculate derivatives of basic functions, …

So, roughly speaking, we have shown that a single variable function is differentiable if and only the difference between f(x) and its linear approximation goes to 0 quickly as x approaches a.