Question

Finding the derivative of $y=\sin\left(t+\cos\left(\sqrt{t}\,\right)\right)$ using the chain rule

score 330 · Answer 1 · 2026-04-15 11:33:25

330

Views

Finding the derivative of $y=\sin\left(t+\cos\left(\sqrt{t}\,\right)\right)$ using the chain rule

Published on 15 Apr 2026 - 11:33

score 78 · Answer 2 · 2026-04-16 18:59:17

78

Views

second derivative $\mbox{Tr} \left(\left(X^{\frac{3}{2}}AX^{\frac{3}{2}}\right)^{\frac{1}{2}}\right)$ with respect to $X$

Published on 16 Apr 2026 - 18:59

score 322 · Answer 3 · 2026-03-25 09:50:07

322

Views

Does equality of (weak) gradients imply equality of functions up to a constant?

Published on 25 Mar 2026 - 9:50

score 148 · Answer 4 · 2026-04-22 23:43:22

148

Views

For which values of $\alpha$ is the disk $B = \{(x, y) \mid x^2+y^2 \leq 1\}$ positively invariant?

Published on 22 Apr 2026 - 23:43

score 36 · Answer 5 · 2026-04-11 06:11:21

36

Views

How to solve this for any constant k?

Published on 11 Apr 2026 - 6:11

score 50 · Answer 6 · 2026-04-15 19:13:09

50

Views

Continuity of partial derivatives of $f(x,y)^t:= \frac{x^2y}{x^6+2y^2} $ when $(x,y)^t\neq (0,0)^t $ and $0$ otherwise

Published on 15 Apr 2026 - 19:13

score 83 · Answer 7 · 2026-04-16 04:47:19

83

Views

For any two functions $f_1 : [0,1] →\mathbb R$ and $f_2 : [0,1] →\mathbb R$, check which among the statements are true.

Published on 16 Apr 2026 - 4:47

score 43 · Answer 8 · 2026-04-17 07:50:58

43

Views

$f(x):=\ln\sqrt {(x_1-\zeta_1)^2+(x_2-\zeta_2)^2}$. $f \in C^2(\mathbb{R}^2\setminus \{0\})$?

Published on 17 Apr 2026 - 7:50

score 68 · Answer 9 · 2026-04-17 23:21:57

68

Views

For $f$ continuous in $[0,1]$, differentiable in $(0,1)$ s.t. $f(0)=0$, prove $|f'(x_0)|\geq |f(x)|$ for some $x_0$ and all $x$ in $[0,1]$

Published on 17 Apr 2026 - 23:21

score 128 · Answer 10 · 2026-04-16 20:24:17

128

Views

If $g$ is 2 times differentiable in $[a,b]$ and $g''+g'\,g=g$ and $g(a)=g(b)=0$, prove that $g=0$.

Published on 16 Apr 2026 - 20:24

score 46 · Answer 11 · 2026-04-25 19:38:46

46

Views

Counterexample to equivalence of definitions of differentiability

Published on 25 Apr 2026 - 19:38

score 808 · Answer 12 · 2026-04-25 11:33:53

808

Views

Equidifferentiable iff derivative is equicontinuous?

Published on 25 Apr 2026 - 11:33

score 1.1k · Answer 13 · 2026-04-11 18:39:36

1.1k

Views

How to find the derivative of this function?

Published on 11 Apr 2026 - 18:39

score 81 · Answer 14 · 2026-04-15 00:59:02

81

Views

Is this the correct way to find the value of $(-1)^{1/2}$?

Published on 15 Apr 2026 - 0:59

score 137 · Answer 15 · 2026-04-11 19:40:38

137

Views

Major notation doubt in calculus.

Published on 11 Apr 2026 - 19:40

List Question

Finding the derivative of $y=\sin\left(t+\cos\left(\sqrt{t}\,\right)\right)$ using the chain rule

second derivative $\mbox{Tr} \left(\left(X^{\frac{3}{2}}AX^{\frac{3}{2}}\right)^{\frac{1}{2}}\right)$ with respect to $X$

Does equality of (weak) gradients imply equality of functions up to a constant?

For which values of $\alpha$ is the disk $B = \{(x, y) \mid x^2+y^2 \leq 1\}$ positively invariant?

How to solve this for any constant k?

Continuity of partial derivatives of $f(x,y)^t:= \frac{x^2y}{x^6+2y^2} $ when $(x,y)^t\neq (0,0)^t $ and $0$ otherwise

For any two functions $f_1 : [0,1] →\mathbb R$ and $f_2 : [0,1] →\mathbb R$, check which among the statements are true.

$f(x):=\ln\sqrt {(x_1-\zeta_1)^2+(x_2-\zeta_2)^2}$. $f \in C^2(\mathbb{R}^2\setminus \{0\})$?

For $f$ continuous in $[0,1]$, differentiable in $(0,1)$ s.t. $f(0)=0$, prove $|f'(x_0)|\geq |f(x)|$ for some $x_0$ and all $x$ in $[0,1]$

If $g$ is 2 times differentiable in $[a,b]$ and $g''+g'\,g=g$ and $g(a)=g(b)=0$, prove that $g=0$.

Counterexample to equivalence of definitions of differentiability

Equidifferentiable iff derivative is equicontinuous?

How to find the derivative of this function?

Is this the correct way to find the value of $(-1)^{1/2}$?

Major notation doubt in calculus.

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