# Tagged Questions

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

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### Show Each function is equivalent using 2 conditions.(Real analysis)

It is might be easy for you. The Question There are functions $f, g, c, s$ $f,g : R \rightarrow R$ and $s,c : R \rightarrow R$ ($R$ is a set of the real number) These functions satisfy ...
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### $f$ be a smooth function on real line , $f(0)=0$ , $f(x)>0, \forall x \ne 0$ and any $f^{(n)}(0)=0$ ; is $\sqrt f$ smooth?

Let $f: \mathbb R \to \mathbb R$ be an infinitely differentiable function such that $f(0)=0$ , $f(x)>0 , \forall x \ne 0$ and $f^{(n)}(0)=0$ ( the $n$-th derivative ) $, \forall n \in \mathbb N$ ...
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### Intuition behind the derivative of are of a square? How to properly use the derivative ?

If I derive the formula $$S=16t^2$$, where S denotes the distance and t denotes time I get $$ds/dt= 32t$$. This in return give me a formula for the speed of the object at any time t. However if we ...
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I was looking at a question that asks for the derivative of $\arcsin (\frac {x+1}{x-1})$. The solution starts by saying $y = \frac{x+1}{x-1}$, so $1-y^2= \frac{4x}{(x+1)^2}$ and $\frac{1}{\sqrt{1-y^... 1answer 47 views ### How many solutions does$a^x=2016x$for$a > 0$have? How many solutions does$a^x=2016x$for$a > 0$and$x \in \mathbb{R}$have? Note that for$x < 0$we have$a^x > 0$and$2016x < 0$so we can consider only$x \ge 0$. Let$f(x) = 2016x - ...
Proof that $\Delta u(x,y):=\partial_1\partial_1u(x,y)+\partial_2\partial_2u(x,y)=0$ is valid for $\log(x^2+y^2)$ and $\arctan\left(\frac{x}{y}\right)$. Is it enough to differentiate the functions in ...
I am trying to derive the following expression w.r.t. $\beta$: $$RSS(\beta) = (\mathbf{y} - \mathbf{X} \beta)^T (\mathbf{y} - \mathbf{X} \beta)$$ I know that the ...