de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative f(x)= 1/((x^3+8)^5)

Lösung

ableitung von

f (x) = \frac{1}{( x ^{3} + 8 ) ^{5}}

Lösung

- \frac{15 x ^{2}}{( x ^{3} + 8 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( x ^{3} + 8 ) ^{5}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{3} + 8)^{- 5})

Wende die Kettenregel an:

- \frac{5}{( x ^{3} + 8 ) ^{6}} \frac{d}{d x} (x^{3} + 8)

= - \frac{5}{( x ^{3} + 8 ) ^{6}} \frac{d}{d x} (x^{3} + 8)

\frac{d}{d x} (x^{3} + 8) = 3 x^{2}

= - \frac{5}{( x ^{3} + 8 ) ^{6}} \cdot 3 x^{2}

Vereinfache

- \frac{5}{( x ^{3} + 8 ) ^{6}} \cdot 3 x^{2} : - \frac{15 x ^{2}}{( x ^{3} + 8 ) ^{6}}

= - \frac{15 x ^{2}}{( x ^{3} + 8 ) ^{6}}

Graph

Beliebte Beispiele

derivative of (sec(x)/(8+sec(x)))

derivative f(x)=-csc(x)cot(x)

derivative of cos(kx)

integral of (sqrt(1+sin(x)))/(sec(x))