Question

Is there a function $f:[0;1]\rightarrow \Bbb R ^n$ of class $C^ \infty$ with $f^{(i)}(0)=10^i.f^{(i)}(1) \, \forall \, i \in \Bbb N_0$

score 121 · Answer 1 · 2026-04-16 04:48:19

Is there a function $f:[0;1]\rightarrow \Bbb R ^n$ of class $C^ \infty$ with $f^{(i)}(0)=10^i.f^{(i)}(1) \, \forall \, i \in \Bbb N_0$

score 212 · Answer 2 · 2026-04-16 20:23:51

212

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If $f(x,y) = g(r)$, where $r=(x^2+y^2)^{1/2}$, prove $\frac{\partial^2f}{\partial x^2} + \frac{\partial^2f}{\partial y^2} = \frac 1r g'(r)+ g''(r).$

Published on 16 Apr 2026 - 20:23

score 28 · Answer 3 · 2026-04-12 05:53:38

28

Views

How are multi-term products involving differential operators calculated?

Published on 12 Apr 2026 - 5:53

score 1.5k · Answer 4 · 2026-04-17 14:52:38

1.5k

Views

Gradient and Hessian of $\sum_i \log \left(1 + \exp\left\{ -t_i \left(w^T x_i\right)\right\} \right) + \mu \|w \|_2^2$?

Published on 17 Apr 2026 - 14:52

score 51 · Answer 5 · 2026-04-16 19:13:07

51

Views

Solution to ODE is bounded $x(t) < 3+e^{t^3-t}$

Published on 16 Apr 2026 - 19:13

score 93 · Answer 6 · 2026-04-08 20:28:11

93

Views

How to prove it without using the expression of $F'(x)$ , using the mean value theorem two times

Published on 08 Apr 2026 - 20:28

score 1.7k · Answer 7 · 2026-04-12 10:41:24

1.7k

Views

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Published on 12 Apr 2026 - 10:41

score 47 · Answer 8 · 2026-04-15 21:31:32

47

Views

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Published on 15 Apr 2026 - 21:31

score 36 · Answer 9 · 2026-04-16 13:37:10

36

Views

Second order differential for change of variable?

Published on 16 Apr 2026 - 13:37

score 223 · Answer 10 · 2026-05-16 16:37:31

223

Views

Find the derivative of $f(\beta) = (\vec{y} -X\beta)^T(\vec{y} -X\beta)$ using the product rule

Published on 16 May 2026 - 16:37

score 530 · Answer 11 · 2026-04-14 06:05:53

530

Views

Derivative of the Cayley Transform.

Published on 14 Apr 2026 - 6:05

score 189 · Answer 12 · 2026-04-15 15:24:06

189

Views

Using the chain rule to guess the derivative of $\frac{1}{x}$

Published on 15 Apr 2026 - 15:24

score 37 · Answer 13 · 2026-04-11 07:19:46

37

Views

Rate of change of sphere

Published on 11 Apr 2026 - 7:19

score 1k · Answer 14 · 2026-04-16 13:32:31

1k

Views

Derivative of $\mathbf{XX}^T$ with respect to $\mathbf{X}$

Published on 16 Apr 2026 - 13:32

score 109 · Answer 15 · 2026-04-11 17:37:58

109

Views

Analytically determine if $f(x) = f'(x)$ is possible?

Published on 11 Apr 2026 - 17:37

List Question

Is there a function $f:[0;1]\rightarrow \Bbb R ^n$ of class $C^ \infty$ with $f^{(i)}(0)=10^i.f^{(i)}(1) \, \forall \, i \in \Bbb N_0$

If $f(x,y) = g(r)$, where $r=(x^2+y^2)^{1/2}$, prove $\frac{\partial^2f}{\partial x^2} + \frac{\partial^2f}{\partial y^2} = \frac 1r g'(r)+ g''(r).$

How are multi-term products involving differential operators calculated?

Gradient and Hessian of $\sum_i \log \left(1 + \exp\left\{ -t_i \left(w^T x_i\right)\right\} \right) + \mu \|w \|_2^2$?

Solution to ODE is bounded $x(t) < 3+e^{t^3-t}$

How to prove it without using the expression of $F'(x)$ , using the mean value theorem two times

When to use different formulas to find the slope of a tangent line

Second order Non-homogeneous differential equations

Second order differential for change of variable?

Find the derivative of $f(\beta) = (\vec{y} -X\beta)^T(\vec{y} -X\beta)$ using the product rule

Derivative of the Cayley Transform.

Using the chain rule to guess the derivative of $\frac{1}{x}$

Rate of change of sphere

Derivative of $\mathbf{XX}^T$ with respect to $\mathbf{X}$

Analytically determine if $f(x) = f'(x)$ is possible?

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