de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of 1/(9x^{8/9})

Lösung

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

Lösung

- \frac{8}{81 x ^{\frac{17}{9}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

\frac{1}{9} (- \frac{8}{9} x^{- \frac{8}{9} - 1}) : - \frac{8}{81 x ^{\frac{17}{9}}}

= - \frac{8}{81 x ^{\frac{17}{9}}}

Graph

Beliebte Beispiele

derivative of 2/((x+2^3))

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

(\partial)/(\partial x)(7-x^2+xy-2y^2)

\frac{\partial}{\partial x} (7 - x^{2} + x y - 2 y^{2})

derivative of 6x^{-2}

\frac{d}{d x} (6 x^{- 2})

tangent 4x-x^2,(1.3)

t an g e n t 4 x - x^{2}, (1.3)

derivative f(x)=5x^4-6x^2+1

d er i v a t i v e f (x) = 5 x^{4} - 6 x^{2} + 1