Show that if (R) is a gradient system then $\frac{\partial f_i}{\partial x_i}-\frac{\partial f_j}{\partial x_j}=0.$
56936
$\frac{\partial f_i}{x_j}=\frac{\partial f_j}{x_i}\implies(f_1,\ldots,f_n)$ is a gradient
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
43956
Differentiating $f(x)^{g(x)}$
74583
Prove that $f'(0)=L$.
45363
Show that both mixed partial derivatives exist at the origin but are not equal
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
36133
Show that $\inf(\frac{1}{n})=0$.
96022
Symmetry of second derivative - Sufficiency of twice-differentiability
136714
Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$.
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
12726
Differentiating both sides of a non-differential equation
53640
Equality of mixed partial derivatives
32506
Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied .
152916
What is the gradient with respect to a vector $\mathbf x$?
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
100608
Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
44761
Is $f'(x)-3f(x) = 0$ subspace of differentiable functions $f\colon (0,1)\to \mathbb{R}$