derivative of sqrt(x^2-3x+12)

Lösung

\frac{d}{d x} (x^{2} - 3 x + 12)

\frac{2 x - 3}{2 x ^{2} - 3 x + 12}

Schritte zur Lösung

\frac{d}{d x} (x^{2} - 3 x + 12)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} - 3 x + 12} \frac{d}{d x} (x^{2} - 3 x + 12)

= \frac{1}{2 x ^{2} - 3 x + 12} \frac{d}{d x} (x^{2} - 3 x + 12)

\frac{d}{d x} (x^{2} - 3 x + 12) = 2 x - 3

= \frac{1}{2 x ^{2} - 3 x + 12} (2 x - 3)

Vereinfache

\frac{1}{2 x ^{2} - 3 x + 12} (2 x - 3) : \frac{2 x - 3}{2 x ^{2} - 3 x + 12}

= \frac{2 x - 3}{2 x ^{2} - 3 x + 12}

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