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Beliebt Rechnen >

derivative ln(4x^3+x)

Lösung

ableitung von

ln (4 x^{3} + x)

Lösung

\frac{12 x ^{2} + 1}{4 x ^{3} + x}

Schritte zur Lösung

\frac{d}{d x} (ln (4 x^{3} + x))

Wende die Kettenregel an:

\frac{1}{4 x ^{3} + x} \frac{d}{d x} (4 x^{3} + x)

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

\frac{d}{d x} (4 x^{3} + x) = 12 x^{2} + 1

= \frac{1}{4 x ^{3} + x} (12 x^{2} + 1)

Vereinfache

\frac{1}{4 x ^{3} + x} (12 x^{2} + 1) : \frac{12 x ^{2} + 1}{4 x ^{3} + x}

= \frac{12 x ^{2} + 1}{4 x ^{3} + x}

Graph

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