derivative-1/6 (x^{-6}-x^{12})

Lösung

ableitung von

- \frac{1}{6} (x^{- 6} - x^{12})

\frac{2 x ^{18} + 1}{x ^{7}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{1}{6} (x^{- 6} - x^{12}))

Entferne die Konstante:

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

= - \frac{1}{6} \frac{d}{d x} (x^{- 6} - x^{12})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{1}{6} (\frac{d}{d x} (x^{- 6}) - \frac{d}{d x} (x^{12}))

\frac{d}{d x} (x^{- 6}) = - \frac{6}{x ^{7}}

\frac{d}{d x} (x^{12}) = 12 x^{11}

= - \frac{1}{6} (- \frac{6}{x ^{7}} - 12 x^{11})

Vereinfache

- \frac{1}{6} (- \frac{6}{x ^{7}} - 12 x^{11}) : \frac{2 x ^{18} + 1}{x ^{7}}

= \frac{2 x ^{18} + 1}{x ^{7}}

\int_{0}^{\frac{π}{7}} sin^{4} (7 x) d x

\frac{d}{d x} (arcsin (sin (13 x)))

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

s im pl i f y - \frac{x}{y}

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