derivative of (x^{1/2}/(\sqrt[3]{x)})

Lösung

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

\frac{1}{6 x ^{\frac{5}{6}}}

Schritte zur Lösung

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

Vereinfache

\frac{x ^{\frac{1}{2}}}{3 x} : x^{\frac{1}{6}}

= \frac{d}{d x} (x^{\frac{1}{6}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{6} x^{\frac{1}{6} - 1}

Vereinfache

\frac{1}{6} x^{\frac{1}{6} - 1} : \frac{1}{6 x ^{\frac{5}{6}}}

= \frac{1}{6 x ^{\frac{5}{6}}}

a re a tan (3 x), 2 sin (3 x), [- \frac{π}{9}, \frac{π}{9}]

d er i v a t i v e y = \frac{x - 1}{x + 1}

\int \frac{( 4 x - 11 )}{( x ^{3} - 9 x ^{2} )} d x

\frac{d}{d x} (cos (wt) + sin (wt))

n = 5 \sum \infty \frac{1}{n + 25}