derivative f(x)=sqrt(2x^2-x)

Lösung

ableitung von

f (x) = 2 x^{2} - x

\frac{4 x - 1}{2 2 x ^{2} - x}

Schritte zur Lösung

\frac{d}{d x} (2 x^{2} - x)

Wende die Kettenregel an:

\frac{1}{2 2 x ^{2} - x} \frac{d}{d x} (2 x^{2} - x)

= \frac{1}{2 2 x ^{2} - x} \frac{d}{d x} (2 x^{2} - x)

\frac{d}{d x} (2 x^{2} - x) = 4 x - 1

= \frac{1}{2 2 x ^{2} - x} (4 x - 1)

Vereinfache

\frac{1}{2 2 x ^{2} - x} (4 x - 1) : \frac{4 x - 1}{2 2 x ^{2} - x}

= \frac{4 x - 1}{2 2 x ^{2} - x}