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Equality of Mixed Partial Derivatives - Simple proof is Confusing

score 213 · Answer 1 · 2026-04-09 18:28:29

213

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Equality of Mixed Partial Derivatives - Simple proof is Confusing

Published on 09 Apr 2026 - 18:28

score 257 · Answer 2 · 2026-04-04 09:43:57

257

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How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?

Published on 04 Apr 2026 - 9:43

score 529 · Answer 3 · 2026-04-04 21:09:41

529

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Proving the differentiability of the following function of two variables

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score 208 · Answer 4 · 2026-04-09 19:27:40

208

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Published on 09 Apr 2026 - 19:27

score 100 · Answer 5 · 2026-04-09 16:26:06

100

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Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$

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score 87 · Answer 6 · 2026-04-05 11:00:36

87

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Number of roots of the e

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score 100 · Answer 7 · 2026-04-08 08:51:47

100

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Published on 08 Apr 2026 - 8:51

score 59 · Answer 8 · 2026-04-05 12:00:31

59

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Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?

Published on 05 Apr 2026 - 12:00

score 119 · Answer 9 · 2026-04-04 00:07:31

119

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How to prove $\frac 10 \notin \mathbb R $

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score 86 · Answer 10 · 2026-04-08 17:31:13

86

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score 162 · Answer 11 · 2026-03-29 10:57:25

162

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score 1.6k · Answer 12 · 2026-04-03 15:25:17

1.6k

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Holding intermediate variables constant in partial derivative chain rule

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score 198 · Answer 13 · 2026-04-02 04:22:26

198

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score 207 · Answer 14 · 2026-04-08 22:24:46

207

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Forgot the name of a common theorem in calculus

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score 2k · Answer 15 · 2026-04-08 22:41:39

2k

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Newton's method with no real roots

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List Question

Equality of Mixed Partial Derivatives - Simple proof is Confusing

How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?

Proving the differentiability of the following function of two variables

If $f ◦f$ is differentiable, then $f ◦f ◦f$ is differentiable

Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$

Number of roots of the e

What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$

Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?

How to prove $\frac 10 \notin \mathbb R $

Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$

Calculation of distance of a point from a curve

Holding intermediate variables constant in partial derivative chain rule

How to prove that $\pi^{e^{\pi^e}}<e^{\pi^{e^{\pi}}}$

Forgot the name of a common theorem in calculus

Newton's method with no real roots

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