Question

Show that $f(x,y)$=$\sqrt[3]{\lvert x^2-(y+1)^2 \lvert}\sin(\lvert x+y+1 \lvert))$ is differentiable at $(0,-1)$, $(1,0)$ and $(-1,0)$

score 52 · Answer 1 · 2026-04-17 08:15:27

52

Views

Show that $f(x,y)$=$\sqrt[3]{\lvert x^2-(y+1)^2 \lvert}\sin(\lvert x+y+1 \lvert))$ is differentiable at $(0,-1)$, $(1,0)$ and $(-1,0)$

Published on 17 Apr 2026 - 8:15

score 116 · Answer 2 · 2026-05-10 16:56:45

116

Views

Calculating the derivative of a mapping $\varphi: S^2 \rightarrow S^2$

Published on 10 May 2026 - 16:56

score 1.6k · Answer 3 · 2026-04-13 16:47:19

1.6k

Views

The derivative of a function raised to the nth power

Published on 13 Apr 2026 - 16:47

score 77 · Answer 4 · 2026-04-14 17:32:56

77

Views

Derivative of $\sqrt{3y-1}=5xy$

Published on 14 Apr 2026 - 17:32

score 502 · Answer 5 · 2026-05-10 19:04:31

502

Views

Differentiability in the complex plane and in $\Bbb R^2$.

Published on 10 May 2026 - 19:04

score 98 · Answer 6 · 2026-04-14 08:35:34

98

Views

Numerical differentiation of functions defined by algorithms

Published on 14 Apr 2026 - 8:35

score 1.9k · Answer 7 · 2026-04-11 00:51:04

1.9k

Views

Contradiction between first derivative formal definition and derivative rules?

Published on 11 Apr 2026 - 0:51

score 60 · Answer 8 · 2026-04-22 05:53:18

60

Views

Find $y'$ where $y=\ln(x+\sqrt{a^2+x^2}).$

Published on 22 Apr 2026 - 5:53

score 55 · Answer 9 · 2026-04-16 11:00:18

55

Views

Is the integral of $\frac{dx}{dt} \cdot f(x) dt$ equal to the derivative of $f(x)$ with respect to $x$?

Published on 16 Apr 2026 - 11:00

score 426 · Answer 10 · 2026-04-13 18:25:34

426

Views

Question about a function that is a ratio of gamma functions and appears to be strictly increasing for $x\ge 2$

Published on 13 Apr 2026 - 18:25

score 38 · Answer 11 · 2026-04-14 12:08:38

38

Views

Find an example of a function f such that Lim(h->0) [f(c+h)-f(c-h)]/2h = L but f'(c)≠L?

Published on 14 Apr 2026 - 12:08

score 179 · Answer 12 · 2026-04-13 13:54:14

179

Views

Necessary conditions for a function to have an antiderivative

Published on 13 Apr 2026 - 13:54

score 108 · Answer 13 · 2026-04-15 20:35:42

108

Views

Proving $(x^4-y^4) \cos (\frac{1}{\left\lVert (x,y) \right\rVert^3_2})$ is totally differentiable

Published on 15 Apr 2026 - 20:35

score 512 · Answer 14 · 2026-04-16 15:13:58

512

Views

Proving continuity in the origin $\frac{xy}{\sqrt{x^2 + y^2}}$

Published on 16 Apr 2026 - 15:13

score 121 · Answer 15 · 2026-04-11 16:53:00

121

Views

Directional derivative of differentiable function on a line segment

Published on 11 Apr 2026 - 16:53

List Question

Show that $f(x,y)$=$\sqrt[3]{\lvert x^2-(y+1)^2 \lvert}\sin(\lvert x+y+1 \lvert))$ is differentiable at $(0,-1)$, $(1,0)$ and $(-1,0)$

Calculating the derivative of a mapping $\varphi: S^2 \rightarrow S^2$

The derivative of a function raised to the nth power

Derivative of $\sqrt{3y-1}=5xy$

Differentiability in the complex plane and in $\Bbb R^2$.

Numerical differentiation of functions defined by algorithms

Contradiction between first derivative formal definition and derivative rules?

Find $y'$ where $y=\ln(x+\sqrt{a^2+x^2}).$

Is the integral of $\frac{dx}{dt} \cdot f(x) dt$ equal to the derivative of $f(x)$ with respect to $x$?

Question about a function that is a ratio of gamma functions and appears to be strictly increasing for $x\ge 2$

Find an example of a function f such that Lim(h->0) [f(c+h)-f(c-h)]/2h = L but f'(c)≠L?

Necessary conditions for a function to have an antiderivative

Proving $(x^4-y^4) \cos (\frac{1}{\left\lVert (x,y) \right\rVert^3_2})$ is totally differentiable

Proving continuity in the origin $\frac{xy}{\sqrt{x^2 + y^2}}$

Directional derivative of differentiable function on a line segment

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