# Tagged Questions

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### Calculus - Find parameters $A,B \in \mathbb R$ such that the function's derivative is $0$ as many times as possible

we are given the function $$f(x)=x+A\frac{x^2-2}{x}+B\frac{x^2-2}{x^3}$$ where $A,B$ are some parameters in $\mathbb R$. We are asked to find the values of $A,B$ such that we have the most ...
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### Characteristics of functions whose second derivative exists on an interval.

If a function $f:\left[a,b\right]\mapsto\mathbb R$ is differentiable on [a,b] and $f':\left[a,b\right]\mapsto\mathbb R$ is differentiable on [a,b] Then do the following statements have to be true? ...
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### Differentiation of improper integral

Differentiate $L$ with respect to $t$, where $L= a(t)\int _{t}^{\infty}\frac{dt}{a(t)}$, and $a$ is a function of $t$. I have seen in a paper that $\frac{d}{dt}L=\frac{\dot{a}}{a}L+1$, but I don't ...
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### Determine the values of $r$ where $f´(0)$ exist.

If $r>0$ is rational, let $f:\mathbb R\to \mathbb R$, whit $f(x)=x^r\cdot\sin(1/x)$ for all $x \neq 0$ and $f(0):=0$, determine the values of $r$ where $f´(0)$ exist. I dont know hoy can I ...
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### Find where the function $k(x):=|\sin(x)|$ is differentiable and calculate its derivative

Find where the function$$k(x):=|\sin(x)|$$ is differentiable and calculate its derivative. I have started, by trying to make a function by parts, because of the absolute value, getting this: ...
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### Help with a simple derivative

I am trying to solve $\dfrac {6} {\sqrt {x^3+6}}$ and so far I made it to $6(x^3+6)^{-\frac 1 2}$ then I continued and now I have $(x^3+6)^{- \frac 3 2} * 3x^2$ and I cannot figure out what how to ...