Question

Is there a smarter way to differentiate the function $f(x) = \sin^{-1} \frac{2x}{1+x^2}$?

score 107 · Answer 1 · 2026-04-16 16:56:09

107

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Is there a smarter way to differentiate the function $f(x) = \sin^{-1} \frac{2x}{1+x^2}$?

Published on 16 Apr 2026 - 16:56

score 125 · Answer 2 · 2026-04-12 10:48:45

125

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calculating a higher order derivative

Published on 12 Apr 2026 - 10:48

score 1.6k · Answer 3 · 2026-04-16 20:47:09

1.6k

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Derivative of inverse function proof verification

Published on 16 Apr 2026 - 20:47

score 125 · Answer 4 · 2026-04-08 18:39:07

125

Views

Intuition behind higher derivatives

Published on 08 Apr 2026 - 18:39

score 115 · Answer 5 · 2026-04-16 19:32:34

115

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If $f(x)=\langle x,a\rangle e^{-\langle x, x\rangle} \ \forall x, a \in \Bbb{R}^{n}$, then prove that $f$ is of class $C^{1}$ and compute $f'(x)$

Published on 16 Apr 2026 - 19:32

score 114 · Answer 6 · 2026-04-16 21:36:59

114

Views

If $f(x,y)=e^{x-y}-x-y-1,\forall\;(x,y)\in\Bbb{R}^2$, then $\exists\;\alpha>0$ and $\varphi:\,]-\alpha,\alpha[\to\Bbb{R}$ of class $\Bbb{C}^{\infty}$

Published on 16 Apr 2026 - 21:36

score 140 · Answer 7 · 2026-03-25 22:06:00

140

Views

Let $f(x^4+8x)=24x$ where $x < 0$, find $f^\prime(0)$

Published on 25 Mar 2026 - 22:06

score 65 · Answer 8 · 2026-04-16 22:39:54

65

Views

Derivatives- Application

Published on 16 Apr 2026 - 22:39

score 115 · Answer 9 · 2026-04-16 22:04:38

115

Views

Prove that $\Vert f(x) -f(y)\Vert\geq (1-k)\Vert x-y\Vert,\;\text{and}\;\Vert f'(x)h\Vert\geq (1-k)\Vert h\Vert,\;\forall\,x,y,h\in\Bbb{R^n}$

Published on 16 Apr 2026 - 22:04

score 199 · Answer 10 · 2026-04-13 09:09:29

199

Views

Matrix differentiation with respect to matrix

Published on 13 Apr 2026 - 9:09

score 3.2k · Answer 11 · 2026-04-17 08:16:09

3.2k

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Find the Fourier series of the function: $f(x)=\begin{cases}x+1 & -1\leq x< 0,\\1-x &0\leq x< 1\end{cases},\;\;f(x+2)=f(x)$

Published on 17 Apr 2026 - 8:16

score 66 · Answer 12 · 2026-04-13 21:54:04

66

Views

Where do we use continuity?

Published on 13 Apr 2026 - 21:54

score 102 · Answer 13 · 2026-04-14 07:44:13

102

Views

Product rule for 3 or more variables?

Published on 14 Apr 2026 - 7:44

score 136 · Answer 14 · 2026-04-12 22:41:34

136

Views

Functional derivative of gradient of cross product

Published on 12 Apr 2026 - 22:41

score 100 · Answer 15 · 2026-04-15 14:21:26

100

Views

$\{u_j\}$ an harmonic sequence, $\{\partial^{\alpha}, |\alpha|\le 2\}$ converges uniformly, $u = \lim_j u_j$ is harmonic in $\Omega$

Published on 15 Apr 2026 - 14:21

List Question

Is there a smarter way to differentiate the function $f(x) = \sin^{-1} \frac{2x}{1+x^2}$?

calculating a higher order derivative

Derivative of inverse function proof verification

Intuition behind higher derivatives

If $f(x)=\langle x,a\rangle e^{-\langle x, x\rangle} \ \forall x, a \in \Bbb{R}^{n}$, then prove that $f$ is of class $C^{1}$ and compute $f'(x)$

If $f(x,y)=e^{x-y}-x-y-1,\forall\;(x,y)\in\Bbb{R}^2$, then $\exists\;\alpha>0$ and $\varphi:\,]-\alpha,\alpha[\to\Bbb{R}$ of class $\Bbb{C}^{\infty}$

Let $f(x^4+8x)=24x$ where $x < 0$, find $f^\prime(0)$

Derivatives- Application

Prove that $\Vert f(x) -f(y)\Vert\geq (1-k)\Vert x-y\Vert,\;\text{and}\;\Vert f'(x)h\Vert\geq (1-k)\Vert h\Vert,\;\forall\,x,y,h\in\Bbb{R^n}$

Matrix differentiation with respect to matrix

Find the Fourier series of the function: $f(x)=\begin{cases}x+1 & -1\leq x< 0,\\1-x &0\leq x< 1\end{cases},\;\;f(x+2)=f(x)$

Where do we use continuity?

Product rule for 3 or more variables?

Functional derivative of gradient of cross product

$\{u_j\}$ an harmonic sequence, $\{\partial^{\alpha}, |\alpha|\le 2\}$ converges uniformly, $u = \lim_j u_j$ is harmonic in $\Omega$

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