Question

Given $0\leq f(x) \leq xh(x)$ and the existence of $\frac{\mathrm d}{\mathrm dx}\big(xh(x)\big)(0)$, can we conclude that $f'(0)$ exists?

score 62 · Answer 1 · 2026-04-16 12:28:54

62

Views

Given $0\leq f(x) \leq xh(x)$ and the existence of $\frac{\mathrm d}{\mathrm dx}\big(xh(x)\big)(0)$, can we conclude that $f'(0)$ exists?

Published on 16 Apr 2026 - 12:28

score 396 · Answer 2 · 2026-04-17 00:55:26

396

Views

What is intuition behind direction of derivative of a function?

Published on 17 Apr 2026 - 0:55

score 511 · Answer 3 · 2026-04-15 17:16:09

511

Views

Is $f(x,y) = \begin{cases}\frac {x^3+y^3}{x^2+y^2}&(x,y)\neq (0,0)\\0& (x,y)=(0,0)\end{cases}$ differentiable at origin?

Published on 15 Apr 2026 - 17:16

score 47 · Answer 4 · 2026-04-12 05:49:09

47

Views

Simplifying integral

Published on 12 Apr 2026 - 5:49

score 61 · Answer 5 · 2026-04-14 22:21:18

61

Views

When is a function of the type $\mathbb{R}^2 \rightarrow \mathbb{R}$ $C^2$?

Published on 14 Apr 2026 - 22:21

score 110 · Answer 6 · 2026-04-16 07:58:31

110

Views

Why is the possibility $x-y = 0$ rejected?

Published on 16 Apr 2026 - 7:58

score 36 · Answer 7 · 2026-04-10 19:48:46

36

Views

Product rule in differentiation

Published on 10 Apr 2026 - 19:48

score 318 · Answer 8 · 2026-04-16 14:35:42

318

Views

Intuitively (or precisely), which functions can be approximated by straight lines?

Published on 16 Apr 2026 - 14:35

score 98 · Answer 9 · 2026-04-16 06:39:02

98

Views

Show, by formal differentiation, $u=e^{-|x|}\circ f$ is a solution to the differential equation $u''-u=-f$

Published on 16 Apr 2026 - 6:39

score 276 · Answer 10 · 2026-04-17 13:43:08

276

Views

Differentiation wrt to a parameter

Published on 17 Apr 2026 - 13:43

score 41 · Answer 11 · 2026-04-15 02:34:55

41

Views

Study derivability in different directions given a point

Published on 15 Apr 2026 - 2:34

score 1.7k · Answer 12 · 2026-04-13 05:42:22

1.7k

Views

Multivariate Mean Value Theorem Reference

Published on 13 Apr 2026 - 5:42

score 59 · Answer 13 · 2026-04-15 18:19:39

59

Views

Define $f^{k}(x) = f(x)^{k}$. Prove that $f^{k}$ is differentiable.

Published on 15 Apr 2026 - 18:19

score 222 · Answer 14 · 2026-04-15 16:58:38

222

Views

Show that $f(x) \geq 1 -x$ if $f(0) \geq 1 $ and $f'(x) \geq -1$

Published on 15 Apr 2026 - 16:58

score 22 · Answer 15 · 2026-04-09 14:09:04

22

Views

Chain rule question-multiple functions in one equation.

Published on 09 Apr 2026 - 14:09

List Question

Given $0\leq f(x) \leq xh(x)$ and the existence of $\frac{\mathrm d}{\mathrm dx}\big(xh(x)\big)(0)$, can we conclude that $f'(0)$ exists?

What is intuition behind direction of derivative of a function?

Is $f(x,y) = \begin{cases}\frac {x^3+y^3}{x^2+y^2}&(x,y)\neq (0,0)\\0& (x,y)=(0,0)\end{cases}$ differentiable at origin?

Simplifying integral

When is a function of the type $\mathbb{R}^2 \rightarrow \mathbb{R}$ $C^2$?

Why is the possibility $x-y = 0$ rejected?

Product rule in differentiation

Intuitively (or precisely), which functions can be approximated by straight lines?

Show, by formal differentiation, $u=e^{-|x|}\circ f$ is a solution to the differential equation $u''-u=-f$

Differentiation wrt to a parameter

Study derivability in different directions given a point

Multivariate Mean Value Theorem Reference

Define $f^{k}(x) = f(x)^{k}$. Prove that $f^{k}$ is differentiable.

Show that $f(x) \geq 1 -x$ if $f(0) \geq 1 $ and $f'(x) \geq -1$

Chain rule question-multiple functions in one equation.

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