A function of a real variable is differentiable at a point of its domain, if its domain contains an open interval containing ⁠⁠, and … See more

If is differentiable at ⁠⁠, then must also be continuous at . As an example, choose a point and let be the step function that returns the value 1 for all less than ⁠⁠, and returns a different value 10 for all greater than or equal to . … See more

One common way of writing the derivative of a function is Leibniz notation, introduced by Gottfried Wilhelm Leibniz in 1675, which denotes a derivative as the quotient of two differentials, such as and ⁠⁠. It is still commonly … See more

In principle, the derivative of a function can be computed from the definition by considering the difference quotient and computing its limit. Once the derivatives of a few simple functions are known, the derivatives … See more

Higher order derivatives are the result of differentiating a function repeatedly. Given that is a differentiable function, the derivative of is the first derivative, denoted as ⁠⁠. The derivative of is the second derivative, … See more