# Tagged Questions

Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem).

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### For every normed space the norm map is not Fréchet differentiable at $0$.

Argue that for every normed space $\mathbb{X} \neq \{ 0 \}$ the norm map $\| \ldotp \|_\mathbb{X} : \mathbb{X} \to \mathbb{R}$ is not Fréchet differentiable at $0$. Not really sure where to start on ...
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### Find the partial derivative of a sphere with equation $x^2+y^2+z^2=4$

We have a sphere with the following equation: $x^2+y^2+z^2=4$ We seek to find the partial derivative, with respect to $x$, of this equation. We think of this equation as a function of three ...
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Which derivatives are eventually periodic? I have noticed that is $a_{n}=f^{(n)}(x)$, the sequence $a_{n}$ becomes eventually periodic for a multitude of $f(x)$. If $f(x)$ was a polynomial, and $... 3answers 56 views ### Limit of derivative does not exist, while limit of difference quotient is infinite Can anyone show an example of a function$f$of a real variabile such that$f$is differentiable on a neighborhood of a point$x_0 \in \mathbb{R}$, except at$x_0$itself;$f$is continuous at$x_0$;... 0answers 14 views ### Derivative with respect to vectors related through a matrix Consider a function$g: \mathbb{R}^r \to \mathbb{R} $and two vectors$\mathbf{b} \in \mathbb{R}^r$and$\mathbf{c} \in \mathbb{R}^m$such that$\mathbf{c} = \mathbf{A}\mathbf{b}$. If I calculate the ... 2answers 64 views ### Can$f''(x)$exist if$f'(x)$is undefined? For example, the piecewise function$ f(x) = \begin{cases} \sqrt{1 - (x + 1)^2} &-2 \leq x \leq 0 \\ -\sqrt{1 - (x - 1)^2} &0 \leq x \leq 2 \end{cases} $will, at$f(0)$, give$f'(0) = $... 0answers 21 views ### Derivative of equation in matrix form I need to compute first derivatives of the following function$S(w)$with respect to$w$. Then solve it. The reason behind that is to minimize$S(w)$.$S(w)=\sum_{i=1}^{n} w_i^{1/2} \bigg(y_i - \sum_{...
I want to find the extreme values of the function $f(x,y,z) = 2x + 2y + z$ under the constraints $x^2+y^2+z^2 \le 2$ and $x^2 + y^2 \le z$ The task is to use a parametrization of the two constraints/...