derivative 4x^{-3}+6x^{-8/3}

Lösung

ableitung von

4 x^{- 3} + 6 x^{- \frac{8}{3}}

\frac{- 12 x ^{\frac{11}{3}} - 16 x ^{4}}{x ^{\frac{23}{3}}}

Schritte zur Lösung

\frac{d}{d x} (4 x^{- 3} + 6 x^{- \frac{8}{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x^{- 3}) + \frac{d}{d x} (6 x^{- \frac{8}{3}})

\frac{d}{d x} (4 x^{- 3}) = - \frac{12}{x ^{4}}

\frac{d}{d x} (6 x^{- \frac{8}{3}}) = - \frac{16}{x ^{\frac{11}{3}}}

= - \frac{12}{x ^{4}} - \frac{16}{x ^{\frac{11}{3}}}

Vereinfache

- \frac{12}{x ^{4}} - \frac{16}{x ^{\frac{11}{3}}} : \frac{- 12 x ^{\frac{11}{3}} - 16 x ^{4}}{x ^{\frac{23}{3}}}

= \frac{- 12 x ^{\frac{11}{3}} - 16 x ^{4}}{x ^{\frac{23}{3}}}

\frac{\partial}{\partial x} (arcsin (3 x + y))

d er i v a t i v e f (x) = 6 e^{x} cos (x)

a re a y^{2} = x + 2, y^{2} = 2 - x

d er i v a t i v e f (x) = - \frac{7}{( x - 7 ) ^{2}}

\int sin^{2} (\frac{2 π x}{L}) d x