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Beliebt Rechnen >

derivative of sqrt(4x^3-7x^2)

Lösung

\frac{d}{d x} (4 x^{3} - 7 x^{2})

Lösung

\frac{6 x - 7}{4 x - 7}

Schritte zur Lösung

\frac{d}{d x} (4 x^{3} - 7 x^{2})

Wende die Kettenregel an:

\frac{1}{2 4 x ^{3} - 7 x ^{2}} \frac{d}{d x} (4 x^{3} - 7 x^{2})

= \frac{1}{2 4 x ^{3} - 7 x ^{2}} \frac{d}{d x} (4 x^{3} - 7 x^{2})

\frac{d}{d x} (4 x^{3} - 7 x^{2}) = 12 x^{2} - 14 x

= \frac{1}{2 4 x ^{3} - 7 x ^{2}} (12 x^{2} - 14 x)

Vereinfache

\frac{1}{2 4 x ^{3} - 7 x ^{2}} (12 x^{2} - 14 x) : \frac{6 x - 7}{4 x - 7}

= \frac{6 x - 7}{4 x - 7}

Graph

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