Question

What is meant by $\frac{\partial x}{\partial y}\frac{\partial y}{\partial z}\frac{\partial z}{\partial x}=-1$ ? How to interpret it?

score 1.6k · Answer 1 · 2026-04-10 04:33:02

1.6k

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What is meant by $\frac{\partial x}{\partial y}\frac{\partial y}{\partial z}\frac{\partial z}{\partial x}=-1$ ? How to interpret it?

Published on 10 Apr 2026 - 4:33

score 64 · Answer 2 · 2026-04-15 14:29:14

64

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Real differentiable function with sequence of turning points that tend to a limit... can the function be analytic?

Published on 15 Apr 2026 - 14:29

score 720 · Answer 3 · 2026-04-17 06:13:49

720

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Derivative of inverse trigonometric functions: $f(x)=\arcsin\left(2x\sqrt{1-x^2}\right)$

Published on 17 Apr 2026 - 6:13

score 129 · Answer 4 · 2026-04-15 06:03:09

129

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$|f'(x)|\le k|f(x)|$ for some $k$ and $f(a) = 0$ imply that $f(x)$ is zero on $[a,b]$.

Published on 15 Apr 2026 - 6:03

score 173 · Answer 5 · 2026-04-29 12:52:20

173

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Permuting with Sinkhorn normalization: find $\sigma$ s.t. $\bf{min}\frac{dS}{dp}\rightarrow \bf{\sigma} \times \bf{X'}= \bf{X}$

Published on 29 Apr 2026 - 12:52

score 109 · Answer 6 · 2026-04-15 17:12:29

109

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Prove that if $f$ differentiable in $x^$ and $f(x^)=0$, then $\liminf_{x\to x^}\frac{|f(x)|}{||x-x^||}=0$ if $n>1$

Published on 15 Apr 2026 - 17:12

score 179 · Answer 7 · 2026-04-14 08:18:56

179

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Linearity of the derivative operator of polynomials

Published on 14 Apr 2026 - 8:18

score 140 · Answer 8 · 2026-04-14 05:18:32

140

Views

$f$ is a real valued function. $f$ is differentiable at a point. Does that imply $f$ is continuous in a neighbourhood of $a$?

Published on 14 Apr 2026 - 5:18

score 244 · Answer 9 · 2026-04-16 06:55:45

244

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$f $ is differentiable on $(0, 1)$ and $\lim_{x \rightarrow 0} f^{'}(x)=\alpha$ for some $\alpha\in \mathbb{R}$. Show $f^{'}(0) = \alpha$.

Published on 16 Apr 2026 - 6:55

score 76 · Answer 10 · 2026-04-29 12:56:02

76

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Differentiation Under the Integral Sign w Variable Substitution

Published on 29 Apr 2026 - 12:56

score 97 · Answer 11 · 2026-04-14 19:10:57

97

Views

$f^{\prime}$ bounded $\implies |f(x)|\leq C|x|+D$

Published on 14 Apr 2026 - 19:10

score 5.6k · Answer 12 · 2026-04-16 07:30:17

5.6k

Views

Find, from first principles, the derivative of $\log(\sec(x^2))$

Published on 16 Apr 2026 - 7:30

score 227 · Answer 13 · 2026-04-16 09:36:03

227

Views

$e^{-x}f(x)=2+ \int_0^x\sqrt{t^4+1}dt$ function for finding the inverse

Published on 16 Apr 2026 - 9:36

score 1.1k · Answer 14 · 2026-04-14 17:33:36

1.1k

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Deriving the Taylor expansion $f(x+p) = f(x) + \nabla f(x+tp)^Tp$

Published on 14 Apr 2026 - 17:33

score 48 · Answer 15 · 2026-03-25 23:35:57

48

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Explain this answer for differentiating an exponent

Published on 25 Mar 2026 - 23:35

List Question

What is meant by $\frac{\partial x}{\partial y}\frac{\partial y}{\partial z}\frac{\partial z}{\partial x}=-1$ ? How to interpret it?

Real differentiable function with sequence of turning points that tend to a limit... can the function be analytic?

Derivative of inverse trigonometric functions: $f(x)=\arcsin\left(2x\sqrt{1-x^2}\right)$

$|f'(x)|\le k|f(x)|$ for some $k$ and $f(a) = 0$ imply that $f(x)$ is zero on $[a,b]$.

Permuting with Sinkhorn normalization: find $\sigma$ s.t. $\bf{min}\frac{dS}{dp}\rightarrow \bf{\sigma} \times \bf{X'}= \bf{X}$

Prove that if $f$ differentiable in $x^$ and $f(x^)=0$, then $\liminf_{x\to x^}\frac{|f(x)|}{||x-x^||}=0$ if $n>1$

Linearity of the derivative operator of polynomials

$f$ is a real valued function. $f$ is differentiable at a point. Does that imply $f$ is continuous in a neighbourhood of $a$?

$f $ is differentiable on $(0, 1)$ and $\lim_{x \rightarrow 0} f^{'}(x)=\alpha$ for some $\alpha\in \mathbb{R}$. Show $f^{'}(0) = \alpha$.

Differentiation Under the Integral Sign w Variable Substitution

$f^{\prime}$ bounded $\implies |f(x)|\leq C|x|+D$

Find, from first principles, the derivative of $\log(\sec(x^2))$

$e^{-x}f(x)=2+ \int_0^x\sqrt{t^4+1}dt$ function for finding the inverse

Deriving the Taylor expansion $f(x+p) = f(x) + \nabla f(x+tp)^Tp$

Explain this answer for differentiating an exponent

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