derivative of 9/(4\sqrt[4]{x^3})

Lösung

\frac{d}{d x} (\frac{9}{4 4 x ^{3}})

- \frac{27}{16 x ^{\frac{7}{4}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9}{4 4 x ^{3}})

Entferne die Konstante:

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

= \frac{9}{4} \frac{d}{d x} (\frac{1}{4 x ^{3}})

Wende Exponentenregel an:

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

= \frac{9}{4} \frac{d}{d x} ((x^{3})^{- \frac{1}{4}})

Wende die Kettenregel an:

- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} (x^{3})

= - \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} (x^{3})

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

= \frac{9}{4} (- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \cdot 3 x^{2})

Vereinfache

\frac{9}{4} (- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \cdot 3 x^{2}) : - \frac{27}{16 x ^{\frac{7}{4}}}

= - \frac{27}{16 x ^{\frac{7}{4}}}

\int \frac{2 x ^{2} - x}{x ^{2} - x + 2} d x

\int 2 x e^{x} d x

\int (2 x - 1) y^{2} sin (4 x y) d x

d er i v a t i v e f (x) = 8 x - 3

t an g e n t f (x) = 2 e^{x} cos (x), at x = 0