derivative of ln(5x^4+4x)

Lösung

\frac{d}{d x} (ln (5 x^{4} + 4 x))

\frac{20 x ^{3} + 4}{5 x ^{4} + 4 x}

Schritte zur Lösung

\frac{d}{d x} (ln (5 x^{4} + 4 x))

Wende die Kettenregel an:

\frac{1}{5 x ^{4} + 4 x} \frac{d}{d x} (5 x^{4} + 4 x)

= \frac{1}{5 x ^{4} + 4 x} \frac{d}{d x} (5 x^{4} + 4 x)

\frac{d}{d x} (5 x^{4} + 4 x) = 20 x^{3} + 4

= \frac{1}{5 x ^{4} + 4 x} (20 x^{3} + 4)

Vereinfache

\frac{1}{5 x ^{4} + 4 x} (20 x^{3} + 4) : \frac{20 x ^{3} + 4}{5 x ^{4} + 4 x}

= \frac{20 x ^{3} + 4}{5 x ^{4} + 4 x}

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