Question

Prove that $f$ and $g$ are differentiable on $\Bbb{R}^n$ and $\Bbb{R}^n-\{0\}$, respectively and compute $f'(x)$ and $g'(x)$

score 60 · Answer 1 · 2026-04-15 23:27:24

60

Views

Prove that $f$ and $g$ are differentiable on $\Bbb{R}^n$ and $\Bbb{R}^n-\{0\}$, respectively and compute $f'(x)$ and $g'(x)$

Published on 15 Apr 2026 - 23:27

score 82 · Answer 2 · 2026-04-16 09:41:27

82

Views

Showing that the function $F(x)=\sum_{n=1}^\infty e^{-nx}\cos n\pi x$ is differentiable on the interval $[0,\infty)$

Published on 16 Apr 2026 - 9:41

score 74 · Answer 3 · 2026-04-17 11:39:18

74

Views

Justifying $\int_{0}^{1}\frac{\partial^n}{\partial m^n} x^m dx=\frac{\partial^n}{\partial m^n}\int_{0}^{1} x^m dx$

Published on 17 Apr 2026 - 11:39

score 48 · Answer 4 · 2026-04-15 02:49:20

48

Views

Derivative of roots $(f(x,p))$

Published on 15 Apr 2026 - 2:49

score 701 · Answer 5 · 2026-04-13 16:59:55

701

Views

Find the partial derivative of a weighted sum function

Published on 13 Apr 2026 - 16:59

score 62 · Answer 6 · 2026-04-14 21:06:45

62

Views

Proving $V(x) = \frac{|y|^2-|x|^2}{|y-x|^N}$ is harmonic in $\mathbb{R}^N-\{y\}$

Published on 14 Apr 2026 - 21:06

score 36 · Answer 7 · 2026-04-10 20:36:13

36

Views

Study directional derivative for $f(x,y)$ at $(x,y)=(0,1)$

Published on 10 Apr 2026 - 20:36

score 418 · Answer 8 · 2026-04-15 02:54:18

418

Views

Differentiability of $f(x)={x^2\sin{(\dfrac{1}{x})}}$ at $x=0$

Published on 15 Apr 2026 - 2:54

score 97 · Answer 9 · 2026-04-14 21:25:23

97

Views

$f'$ is bounded and $\sup\limits_{c\in O}\Vert f'(c) \Vert<\infty$ if and only if $f$ is globally Lipschitz

Published on 14 Apr 2026 - 21:25

score 66 · Answer 10 · 2026-04-14 18:24:08

66

Views

History of ODE and PDE reference request

Published on 14 Apr 2026 - 18:24

score 762 · Answer 11 · 2026-04-11 03:48:21

762

Views

Do a specific inequality hold under integration?

Published on 11 Apr 2026 - 3:48

score 463 · Answer 12 · 2026-04-29 19:34:15

463

Views

How to find second derivative as output of MATLAB ode45?

Published on 29 Apr 2026 - 19:34

score 89 · Answer 13 · 2026-04-16 07:49:49

89

Views

From derivative of $f$ to squaring $f$

Published on 16 Apr 2026 - 7:49

score 2.3k · Answer 14 · 2026-04-14 18:03:53

2.3k

Views

If $f$ is locally Lipschitz, then for any compact set $K$, $f \mid_K$ is globally Lipschitz

Published on 14 Apr 2026 - 18:03

score 144 · Answer 15 · 2026-04-13 03:01:47

144

Views

How to interpret $\frac{f(x)}{f'(x)}$ being a decreasing function?

Published on 13 Apr 2026 - 3:01

List Question

Prove that $f$ and $g$ are differentiable on $\Bbb{R}^n$ and $\Bbb{R}^n-\{0\}$, respectively and compute $f'(x)$ and $g'(x)$

Showing that the function $F(x)=\sum_{n=1}^\infty e^{-nx}\cos n\pi x$ is differentiable on the interval $[0,\infty)$

Justifying $\int_{0}^{1}\frac{\partial^n}{\partial m^n} x^m dx=\frac{\partial^n}{\partial m^n}\int_{0}^{1} x^m dx$

Derivative of roots $(f(x,p))$

Find the partial derivative of a weighted sum function

Proving $V(x) = \frac{|y|^2-|x|^2}{|y-x|^N}$ is harmonic in $\mathbb{R}^N-\{y\}$

Study directional derivative for $f(x,y)$ at $(x,y)=(0,1)$

Differentiability of $f(x)={x^2\sin{(\dfrac{1}{x})}}$ at $x=0$

$f'$ is bounded and $\sup\limits_{c\in O}\Vert f'(c) \Vert<\infty$ if and only if $f$ is globally Lipschitz

History of ODE and PDE reference request

Do a specific inequality hold under integration?

How to find second derivative as output of MATLAB ode45?

From derivative of $f$ to squaring $f$

If $f$ is locally Lipschitz, then for any compact set $K$, $f \mid_K$ is globally Lipschitz

How to interpret $\frac{f(x)}{f'(x)}$ being a decreasing function?

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