Question

Stuck calculating the derivative of $f(x)=\log_{10}{\frac{x}{1+\sqrt{5-x^2}}}$.

score 52 · Answer 1 · 2026-04-17 11:13:51

52

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Stuck calculating the derivative of $f(x)=\log_{10}{\frac{x}{1+\sqrt{5-x^2}}}$.

Published on 17 Apr 2026 - 11:13

score 142 · Answer 2 · 2026-04-17 15:37:02

142

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If $\frac{\cos^4 \alpha}{x}+\frac{\sin^4 \alpha}{y}=\frac{1}{x+y}$,prove that $\frac{dy}{dx}=\tan^2\alpha$

Published on 17 Apr 2026 - 15:37

score 56 · Answer 3 · 2026-04-14 21:26:34

56

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Are vectors and the derivative of $\left|x\right|$ related?

Published on 14 Apr 2026 - 21:26

score 30 · Answer 4 · 2026-04-14 04:38:41

30

Views

Find f(x) using definition of differentiability

Published on 14 Apr 2026 - 4:38

score 96 · Answer 5 · 2026-04-16 11:45:47

96

Views

$f$ differentiable, $|f|$ constant $\Longrightarrow \det J_{f} = 0$.

Published on 16 Apr 2026 - 11:45

score 143 · Answer 6 · 2026-04-15 10:29:22

143

Views

Trouble calculating the limit $\lim_{x\to\infty} \frac{e^{-x}}{x^{-1}}$

Published on 15 Apr 2026 - 10:29

score 161 · Answer 7 · 2026-04-13 22:00:50

161

Views

Derivatives for non Real/Complex functions

Published on 13 Apr 2026 - 22:00

score 63 · Answer 8 · 2026-04-10 02:14:08

63

Views

The difference between $\int$ and $d()$?

Published on 10 Apr 2026 - 2:14

score 222 · Answer 9 · 2026-04-14 01:18:39

222

Views

Infinitely many times differentiable function, whose every derivative approaches zero at x boundaries

Published on 14 Apr 2026 - 1:18

score 1.5k · Answer 10 · 2026-04-15 20:02:03

1.5k

Views

Inverse L'hospital.... does it exist?

Published on 15 Apr 2026 - 20:02

score 59 · Answer 11 · 2026-04-08 21:13:57

59

Views

Finding change of temperature at $t = 0$

Published on 08 Apr 2026 - 21:13

score 89 · Answer 12 · 2026-04-13 13:10:37

89

Views

If $f''$ exists on an interval centered at $x=a$, then $\lim \limits_{h\to 0} \frac{f(a+h) - 2f(a) +f(a-h)}{h^2} = f''(a)$

Published on 13 Apr 2026 - 13:10

score 216 · Answer 13 · 2026-04-14 05:15:10

216

Views

If $x\mapsto \lim_{h\to 0} \frac{f(x+h) - 2f(x) +f(x-h)}{h^2}$ is continuous, then $f\in C^2$

Published on 14 Apr 2026 - 5:15

score 122 · Answer 14 · 2026-04-10 19:20:24

122

Views

$\lim_{h\to 0} \frac{ f(a+ h) - 2f(a) + f(a-h) }{h^2}$ and a polynomial function with degree at most 2

Published on 10 Apr 2026 - 19:20

score 65 · Answer 15 · 2026-04-14 15:48:24

65

Views

Show $\frac{d}{dx}$ is bounded on $C^k[a,b]$

Published on 14 Apr 2026 - 15:48

List Question

Stuck calculating the derivative of $f(x)=\log_{10}{\frac{x}{1+\sqrt{5-x^2}}}$.

If $\frac{\cos^4 \alpha}{x}+\frac{\sin^4 \alpha}{y}=\frac{1}{x+y}$,prove that $\frac{dy}{dx}=\tan^2\alpha$

Are vectors and the derivative of $\left|x\right|$ related?

Find f(x) using definition of differentiability

$f$ differentiable, $|f|$ constant $\Longrightarrow \det J_{f} = 0$.

Trouble calculating the limit $\lim_{x\to\infty} \frac{e^{-x}}{x^{-1}}$

Derivatives for non Real/Complex functions

The difference between $\int$ and $d()$?

Infinitely many times differentiable function, whose every derivative approaches zero at x boundaries

Inverse L'hospital.... does it exist?

Finding change of temperature at $t = 0$

If $f''$ exists on an interval centered at $x=a$, then $\lim \limits_{h\to 0} \frac{f(a+h) - 2f(a) +f(a-h)}{h^2} = f''(a)$

If $x\mapsto \lim_{h\to 0} \frac{f(x+h) - 2f(x) +f(x-h)}{h^2}$ is continuous, then $f\in C^2$

$\lim_{h\to 0} \frac{ f(a+ h) - 2f(a) + f(a-h) }{h^2}$ and a polynomial function with degree at most 2

Show $\frac{d}{dx}$ is bounded on $C^k[a,b]$

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