derivative of \sqrt[3]{ln(x})

Lösung

\frac{d}{d x} (3 ln (x))

\frac{1}{3 x ln ^{\frac{2}{3}} ( x )}

Schritte zur Lösung

\frac{d}{d x} (3 ln (x))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= \frac{1}{3 ( ln ( x ) ) ^{\frac{2}{3}}} \cdot \frac{1}{x}

Vereinfache

\frac{1}{3 ln ^{\frac{2}{3}} ( x )} \cdot \frac{1}{x} : \frac{1}{3 x ln ^{\frac{2}{3}} ( x )}

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

\int 4 sec^{3} (x) d x

\int \frac{3 t}{1 - 9 t ^{4}} d t

\int 3 cos (3 x) d x

t an g e n t f (x) = 5 e^{x} + 7 x, at x = 0

\frac{\partial}{\partial t} (e^{2 x} - x cos (t))