derivative of ln(x^3-1)

Lösung

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

\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}

\int_{- 4}^{2} (12 - x - x^{2}) - (x + 4) d x

\frac{\partial}{\partial x} (x^{5} + 7 x^{5} y)

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

e^{y} y^{^{'}} + \frac{t}{y + 1} = \frac{2}{y + 1}

x \to \infty lim (\frac{1}{6 ^{x + 1}})