Show, using the definition of derivative, that $f:\mathbb{R}^2\rightarrow\mathbb{R}$ defined by $f(x,y)=xy$ is differentiable everywhere.
131357
Prove that $f(x,y)=xy$ is differentiable using the definition
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
138864
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f(x+y)=f(x)f(y)$ and $f'(0)$ exists, then $f$ is differentiable on $\mathbb R$
57407
Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
45071
Having the derivative be an operator
40549
How to proof the the derivative of $x^2$ is $2x$?
111470
Proof of differentiability of $f(x)$
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
152111
Difference between differentiation and derivatives
43956
Differentiating $f(x)^{g(x)}$
53767
How to prove that derivatives have the Intermediate Value Property
4636
How to show that $f$ is differentiable at $x=0.$
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
128921
Why define $(\nabla^2F)(X,Y)=\nabla_X(\nabla_YF)-(\nabla_{\nabla_XY}F)$?
124346
Where is $f(z)=\Re (z)$ differentiable?
156536
Defining functions as derivatives