Question

Proof: There is no function $f \in C^2(\mathbb{R^3})$ with gradient $\nabla f(x,y,z) = (yz, xz, xy^2)$

score 352 · Answer 1 · 2026-04-16 04:31:05

352

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Proof: There is no function $f \in C^2(\mathbb{R^3})$ with gradient $\nabla f(x,y,z) = (yz, xz, xy^2)$

Published on 16 Apr 2026 - 4:31

score 149 · Answer 2 · 2026-04-15 10:39:37

149

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What am I doing wrong finding the derivative of $\frac{3-x}{2}\sqrt{1-2x-x^2}+2\arcsin{\frac{1+x}{\sqrt{2}}}$?

Published on 15 Apr 2026 - 10:39

score 50 · Answer 3 · 2026-04-30 15:23:15

50

Views

Proving that first derivative vanishes

Published on 30 Apr 2026 - 15:23

score 453 · Answer 4 · 2026-04-16 11:06:54

453

Views

Variance of the truncated normal distribution (truncated from below) increases in $\sigma$?

Published on 16 Apr 2026 - 11:06

score 87 · Answer 5 · 2026-04-24 07:40:55

87

Views

Is $g$ differentiable in $0$?

Published on 24 Apr 2026 - 7:40

score 54 · Answer 6 · 2026-04-17 08:13:48

54

Views

Find $F'(x)$ of $F(x)=\int_{\pi e^x}^{\cos(x)} \cos (t) dt$

Published on 17 Apr 2026 - 8:13

score 59 · Answer 7 · 2026-04-14 00:39:13

59

Views

Proving that $|x \, g(y) - y \, g(x)| \leq C$ for $x,y \in [-1,1]$, where $|g''(t)| \leq C$

Published on 14 Apr 2026 - 0:39

score 92 · Answer 8 · 2026-04-14 07:26:11

92

Views

How to determine local extrema for $f(x) = x\cdot \sin(x) ^ {\sin(x)}$

Published on 14 Apr 2026 - 7:26

score 86 · Answer 9 · 2026-04-10 02:34:47

86

Views

Find the error when approximating a function

Published on 10 Apr 2026 - 2:34

score 510 · Answer 10 · 2026-05-10 21:26:51

510

Views

(Why) can we treat a function of a variable as another independent variable?

Published on 10 May 2026 - 21:26

score 171 · Answer 11 · 2026-04-11 14:04:15

171

Views

Differentiability implies continuity proof with little-o notation

Published on 11 Apr 2026 - 14:04

score 104 · Answer 12 · 2026-04-16 08:19:08

104

Views

Solve $T'(x)=45-0.75\cdot T(x)$, where $T(0)=75$.

Published on 16 Apr 2026 - 8:19

score 93 · Answer 13 · 2026-04-15 03:39:55

93

Views

How is $C_0^k(\mathbb R)$ defined?

Published on 15 Apr 2026 - 3:39

score 57 · Answer 14 · 2026-04-16 23:16:53

57

Views

Derivative of $\arctan\big (s-\sqrt{1+s^{2}}\big) $

Published on 16 Apr 2026 - 23:16

score 234 · Answer 15 · 2026-04-14 17:33:36

Given second and first derivatives at 2 points, prove that some point in between them has third derivative greater than or equal to 24.

List Question

Proof: There is no function $f \in C^2(\mathbb{R^3})$ with gradient $\nabla f(x,y,z) = (yz, xz, xy^2)$

What am I doing wrong finding the derivative of $\frac{3-x}{2}\sqrt{1-2x-x^2}+2\arcsin{\frac{1+x}{\sqrt{2}}}$?

Proving that first derivative vanishes

Variance of the truncated normal distribution (truncated from below) increases in $\sigma$?

Is $g$ differentiable in $0$?

Find $F'(x)$ of $F(x)=\int_{\pi e^x}^{\cos(x)} \cos (t) dt$

Proving that $|x \, g(y) - y \, g(x)| \leq C$ for $x,y \in [-1,1]$, where $|g''(t)| \leq C$

How to determine local extrema for $f(x) = x\cdot \sin(x) ^ {\sin(x)}$

Find the error when approximating a function

(Why) can we treat a function of a variable as another independent variable?

Differentiability implies continuity proof with little-o notation

Solve $T'(x)=45-0.75\cdot T(x)$, where $T(0)=75$.

How is $C_0^k(\mathbb R)$ defined?

Derivative of $\arctan\big (s-\sqrt{1+s^{2}}\big) $

Given second and first derivatives at 2 points, prove that some point in between them has third derivative greater than or equal to 24.

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