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

Lösung

ableitung von

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

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

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

d er i v a t i v e \frac{x ^{2} - 36}{x - 6}

y^{^{''}} + y = sin (2 x)

\frac{d}{d x} ((2 x^{2} - 1) + (5 x - 6))

f (x) = 12 x^{2}

\frac{\partial}{\partial x} (10 x^{\frac{1}{4}} \cdot 2 y^{\frac{3}{4}})