We now know how to find formulas for the derivatives of a wide variety of functions; but the derivative is defined by a limit, and while we spent a lot of time worrying about whether various …

Lesson 2.6: Differentiability: Afunctionisdifferentiable at a point if it has a derivative there. In other words: The function f is differentiable at x if lim. h→0. f(x+h)−f(x) h exists. Thus, the …

Extending the definition of differentiability in its present form to functions of several variables is not possible because the definition involves division and dividing by a vector or by a point in n …

We can di erentiate in di erent directions as well as in some overall sense, and these are related in a speci c way, namely by a matrix of partial derivatives. The necessary hypotheses are …

Theorem A, we conclude that 2 f is not differentiable at (0; 0). One can also rely on the definition of differentiability: sup. ose f is differentiable and see if we can obtain a contradiction. If this …

iability for f(x). If f(x) is differentiable at every point in its domain, we say that f(x) is a differentiable func.

Skill Builder: Topics 2.4 – Differentiability 1.) For the following, state whether the function is continuous, differentiable, both or neither at x = c. ... 2.) Sketch a function having the following …