f(x) = \(\frac{x}{2·√(x)}\) = \(\frac{√x}{2}\) , da x = ( √x )2 kann man durch √x kürzen.
f '(x) = \(\frac{1}{2}\) • \(\frac{1}{2·√x}\) = \(\frac{1}{4·√x}\)
Mit Potenz- und Faktorregel:
f (x) = \(\frac{1}{2}\) • x • x-0,5 = \(\frac{1}{2}\) • x0,5
f '(x) = \(\frac{1}{2}\) • \(\frac{1}{2}\) • x- 0,5 = \(\frac{1}{4}\) • \(\frac{1}{√x}\) = \(\frac{1}{4·√x}\)
Gruß Wolfgang