derivative of \sqrt[8]{x^9}

Lösung

\frac{d}{d x} (8 x^{9})

\frac{9 x ^{\frac{1}{8}}}{8}

Schritte zur Lösung

\frac{d}{d x} (8 x^{9})

Wende die Kettenregel an:

\frac{1}{8 ( x ^{9} ) ^{\frac{7}{8}}} \frac{d}{d x} (x^{9})

= \frac{1}{8 ( x ^{9} ) ^{\frac{7}{8}}} \frac{d}{d x} (x^{9})

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{1}{8 ( x ^{9} ) ^{\frac{7}{8}}} \cdot 9 x^{8}

Vereinfache

\frac{1}{8 ( x ^{9} ) ^{\frac{7}{8}}} \cdot 9 x^{8} : \frac{9 x ^{\frac{1}{8}}}{8}

= \frac{9 x ^{\frac{1}{8}}}{8}

\frac{d}{d x} (arctan (x^{4}))

f (t) = \frac{t ^{2} + 1}{t ^{2} - 1}

\int_{1}^{\infty} \frac{1}{5 x + 2} d x

\frac{d}{d x} (lo g_{7} (x^{2}))

\frac{d}{d x} (\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}})