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Beliebt Rechnen >

derivative of ln(x^3-2x^2+2)

Lösung

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

Lösung

\frac{3 x ^{2} - 4 x}{x ^{3} - 2 x ^{2} + 2}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{x ^{3} - 2 x ^{2} + 2} (3 x^{2} - 4 x) : \frac{3 x ^{2} - 4 x}{x ^{3} - 2 x ^{2} + 2}

= \frac{3 x ^{2} - 4 x}{x ^{3} - 2 x ^{2} + 2}

Graph

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