Show that $F(x) = f(\|x\|)$ is differentiable on $\mathbb{R}^n$.
55507
Multivariate differentiability verification
22313
How should I calculate the $n$th derivative of $f(x)=x^x$?
65953
Cardinality of the set of differentiable functions
43956
Differentiating $f(x)^{g(x)}$
56936
$\frac{\partial f_i}{x_j}=\frac{\partial f_j}{x_i}\implies(f_1,\ldots,f_n)$ is a gradient
104263
How to show that $f'(x)<2f(x)$
136714
Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$.
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
27265
Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
27888
Why is $|x|$ not differentiable at $x=0$?
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
85623
Proof of continuity implied by differentiability
77624
Characterization of sets of differentiability
83707
Suppose that $f$ is differentiable on $\mathbb{R}$ and $\lim_{x\to \infty}f'(x)=M$. Show that $\lim_{x\to \infty}f(x+1)-f(x)$ exists and find it.
3387
Derivative of $f(x)=|x|$
91430
If $f$ is twice differentiable, $\big(f(y) - f(x)\big)/(y-x)$ is differentiable
80650
Complex differentiability of $f(z)=|z|$