derivative of sqrt(x^2-x+4)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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