Good job giving the general definition of differentiability, since we can compare it with the definition of derivative in higher dimensions. $\endgroup$ – information_interchange Commented Mar 18, 2020 at 21:11

Differentiability refers to the existence of a derivative while differentiation is the process of taking the derivative. It is like the difference between perceptibility and perception. An object is perceptible if we can perceive it.

2015年8月22日 · Differentiability of $ f(x,y)=\frac{2x^3+3y^3}{x^2+y^2}$ 0 Proving differentiability, continuity and partial derivatives of the following two variables function

How does one prove differentiability? Ask Question Asked 9 years, 3 months ago. Modified 9 years, 3 months ...

Multivariable Calculus and Differentiability. 0. Continuity, partial derivatives and differentiability of ...

$\begingroup$ Continuous partial derivatives imply continuous differentiability, so that is enough. Note that differentiability is a strictly stronger condition than partial differentiability. But if you add continuity, both coincide. $\endgroup$ –

For a function defined on a finite dimensional normed vector space (one can also extend this to the Fréchet derivatives on Banach spaces), we can think of the derivative as a linear approximation to the function.

2019年7月20日 · (From this definition, you can show that differentiability implies continuity). This idea of "linear approximations" has proven to be a very powerful and useful idea in analysis/calculus, and it's why mathematicians have defined differentiability in the manner I have just stated. For example, in single variable calculus, you may have been asked ...

Differentiability means that the function has a derivative at a point. Continuity means that the limit from both sides of a value is equal to the function's value at that point. Share

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