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Beliebt Rechnen >

derivative y=ln(x^3+1)

Lösung

ableitung von

y = ln (x^{3} + 1)

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{x ^{3} + 1} \cdot 3 x^{2}

Vereinfache

\frac{1}{x ^{3} + 1} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} + 1}

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

Graph

Beliebte Beispiele

sum from n=0 to infinity of 1/3

n = 0 \sum \infty \frac{1}{3}

integral from 0 to 1 of (8x^2-2)e^x

\int_{0}^{1} (8 x^{2} - 2) e^{x} d x

d/(dt)((arccos(t))^2)

\frac{d}{d t} ((arccos (t))^{2})

integral of 2cos^3(4x)

\int 2 cos^{3} (4 x) d x

(\partial)/(\partial v)(2uv)

\frac{\partial}{\partial v} (2 uv)