User:Apocryphax64

[edit] $n$ th Derivative of Any Monomial

$f (x) = a x r / t$

$f^n(x)=a\dfrac{(\prod_{i=0}^{n-1} (r-ti))}{t^n}x^{\frac{r}{t}-n}$ $where \frac{r}{t} \not \in \mathbb{P}$

$a + b = t$

$(a + b)(a - b) = t (a - b)$

$a 2 - b 2 = t a - t b$

$a 2 - t a = b 2 - t b$

$a 2 - t a + (t 2) / 4 = b 2 - t b + (t 2) / 4$

$(a - t / 2) 2 = (b - t / 2) 2$

$a - t / 2 = b - t / 2$ (incorrect to assume only positive root)

$a = b$