derivative of 6/(\sqrt[4]{x})

Lösung

\frac{d}{d x} (\frac{6}{4 x})

- \frac{3}{2 x ^{\frac{5}{4}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{6}{4 x})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (\frac{1}{4 x})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 6 \frac{d}{d x} (x^{- \frac{1}{4}})

Wende die Potenzregel an:

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

= 6 (- \frac{1}{4} x^{- \frac{1}{4} - 1})

Vereinfache

6 (- \frac{1}{4} x^{- \frac{1}{4} - 1}) : - \frac{3}{2 x ^{\frac{5}{4}}}

= - \frac{3}{2 x ^{\frac{5}{4}}}

t an g e n t f (x) = 7 x - x^{2}, (1, 6)

\int_{- 1}^{1} \frac{1}{x} d x

a re a y = \frac{x ^{2} + 5}{6 x - x ^{2}}, (1, 5)

\int - 7 lo g_{2} (x) d x

\int e^{x} (x + 1)^{2} d x