Tagged Questions
6
votes
4answers
133 views
What goes wrong in this derivative?
$$ f(x) = \frac{2}{3} x (x^2-1)^{-2/3} $$
and f'(x) is searched.
So, by applying the product rule $ (uv)' = u'v + uv' $ with $ u=(x^2-1)^{-2/3} $ and $ v=\frac{2}{3} x $, so $ u'=-\frac{4}{3} x ...
2
votes
1answer
73 views
Evaluate a certain derivative
Let $\{x_1,\dots,x_n\}$ be pairwise distinct complex numbers and $\{l_1,\dots,l_n\}$ a vector of natural numbers such that $l_1+l_2+\dots+l_n=N$. Let
$$ h_j(x)=\prod_{i\neq j,i=1,\dots, n} ...
0
votes
1answer
325 views
How to find the equation of a graph of a rational function from a set of points?
For example, the data points are:
(1,1)
(2,1/2)
(3,1/3)
(4,1/4)
(5,1/5)
How do I find the equation from those points? Do I look at the common ratio of the y-values or something?
1
vote
1answer
164 views
Perturbations of Rational Numbers
For $a_1,a_2$, $b_1,b_2$ $\in\mathbb{R}^+$, if $a_1<b_1$ , then for any perturbation $\epsilon\in \mathbb{R}^+$,
$$r_1=\frac{a_1+\epsilon}{b_1+\epsilon}>\frac{a_1}{b_1} $$ and if $a_2>b_2$, ...
1
vote
1answer
183 views
Integration of rational functions..
Some rational function is giving me some trouble...
\begin{aligned}
\ \int \frac {x^2-9x+16}{(x-1)(x^2+6x-7)} dx
\end{aligned}
I simplified it like so:
\begin{aligned}
\ \int \frac ...
