Question

If $\gamma : (-1,1) \to \mathrm{O}(n)$ is a differentiable curve with $\gamma (0) = I_n$, then $\gamma ' (0)$ is skew-symmetric

score 68 · Answer 1 · 2026-05-05 00:08:45

68

Views

If $\gamma : (-1,1) \to \mathrm{O}(n)$ is a differentiable curve with $\gamma (0) = I_n$, then $\gamma ' (0)$ is skew-symmetric

Published on 05 May 2026 - 0:08

score 63 · Answer 2 · 2026-04-16 06:16:27

63

Views

Prove that $t\mapsto \frac{d}{dt}\left[\rho(t)\right]^{-1}=-\rho(t)^{-1}\rho'(t)\rho(t)^{-1}$

Published on 16 Apr 2026 - 6:16

score 78 · Answer 3 · 2026-04-15 21:45:09

78

Views

How to find the limit of $\frac{\sin(x^2 + y^2)}{1-\cos \sqrt{x^2+y^2}}$ as $(x,y)\to0$?

Published on 15 Apr 2026 - 21:45

score 42 · Answer 4 · 2026-04-16 10:56:12

42

Views

FInding $f_{xy}$ and $f_{yx}$ given a piecewise function

Published on 16 Apr 2026 - 10:56

score 683 · Answer 5 · 2026-04-15 18:23:06

683

Views

Why doesn't the limit $\lim_{r \to 0} \frac{r (\cos^2\theta\sin\theta)}{r^2\cos^4\theta + \sin^2\theta}$ exist?

Published on 15 Apr 2026 - 18:23

score 1k · Answer 6 · 2026-05-05 00:08:14

1k

Views

How to take the derivative of $f(\lambda x + (1-\lambda)y)$ w.r.t to $\lambda$ for real valued $f$ but $x$ of dimension $n$

Published on 05 May 2026 - 0:08

score 120 · Answer 7 · 2026-05-05 00:05:06

120

Views

Non differentiability of $|x| + |y|$

Published on 05 May 2026 - 0:05

score 84 · Answer 8 · 2026-05-05 00:06:12

84

Views

$f: GL(2, \mathbb{R}) \to GL(2, \mathbb{R)}, \ A\mapsto A^{-1}$. Looking for $df(A)$

Published on 05 May 2026 - 0:06

score 31 · Answer 9 · 2026-04-22 06:25:19

31

Views

Extrema on $D:=\{(a,b)^T \in \mathbb{R}^2: \|(a,b)^T\|_2=1\}$ of $f((a,b)^T)=5a^2+7b^2-14ab$

Published on 22 Apr 2026 - 6:25

score 44 · Answer 10 · 2026-04-14 14:01:07

44

Views

Why are partial derivatives of functions of two variables themselves functions of two variables?

Published on 14 Apr 2026 - 14:01

score 38 · Answer 11 · 2026-04-11 17:08:29

38

Views

Some questions about the definition of differentiability in multivariable Calculus.

Published on 11 Apr 2026 - 17:08

score 99 · Answer 12 · 2026-04-16 15:24:44

99

Views

derivative of $f(x,y)$ w.r.t.$ \ u(x,y)$

Published on 16 Apr 2026 - 15:24

score 78 · Answer 13 · 2026-04-10 04:16:16

78

Views

Continuity of $f(x,y)$ which is not defined along a path

Published on 10 Apr 2026 - 4:16

score 3.4k · Answer 14 · 2026-04-16 22:49:41

3.4k

Views

$f((x,y)^T)=\frac{xy^2}{x^2+y^2}$ not differentiable in $(0,0)^T$

Published on 16 Apr 2026 - 22:49

score 21.9k · Answer 15 · 2026-04-11 21:15:58

21.9k

Views

How to find the tangent line of a level curve of a function?

Published on 11 Apr 2026 - 21:15

List Question

If $\gamma : (-1,1) \to \mathrm{O}(n)$ is a differentiable curve with $\gamma (0) = I_n$, then $\gamma ' (0)$ is skew-symmetric

Prove that $t\mapsto \frac{d}{dt}\left[\rho(t)\right]^{-1}=-\rho(t)^{-1}\rho'(t)\rho(t)^{-1}$

How to find the limit of $\frac{\sin(x^2 + y^2)}{1-\cos \sqrt{x^2+y^2}}$ as $(x,y)\to0$?

FInding $f_{xy}$ and $f_{yx}$ given a piecewise function

Why doesn't the limit $\lim_{r \to 0} \frac{r (\cos^2\theta\sin\theta)}{r^2\cos^4\theta + \sin^2\theta}$ exist?

How to take the derivative of $f(\lambda x + (1-\lambda)y)$ w.r.t to $\lambda$ for real valued $f$ but $x$ of dimension $n$

Non differentiability of $|x| + |y|$

$f: GL(2, \mathbb{R}) \to GL(2, \mathbb{R)}, \ A\mapsto A^{-1}$. Looking for $df(A)$

Extrema on $D:=\{(a,b)^T \in \mathbb{R}^2: \|(a,b)^T\|_2=1\}$ of $f((a,b)^T)=5a^2+7b^2-14ab$

Why are partial derivatives of functions of two variables themselves functions of two variables?

Some questions about the definition of differentiability in multivariable Calculus.

derivative of $f(x,y)$ w.r.t.$ \ u(x,y)$

Continuity of $f(x,y)$ which is not defined along a path

$f((x,y)^T)=\frac{xy^2}{x^2+y^2}$ not differentiable in $(0,0)^T$

How to find the tangent line of a level curve of a function?

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