derivative 1/8 x^4-(32)/(x^3)

Lösung

ableitung von

\frac{1}{8} x^{4} - \frac{32}{x ^{3}}

\frac{x ^{3}}{2} + \frac{96}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{8} x^{4} - \frac{32}{x ^{3}})

Vereinfache

\frac{1}{8} x^{4} - \frac{32}{x ^{3}} : \frac{x ^{4}}{8} - \frac{32}{x ^{3}}

= \frac{d}{d x} (\frac{x ^{4}}{8} - \frac{32}{x ^{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{4}}{8}) - \frac{d}{d x} (\frac{32}{x ^{3}})

\frac{d}{d x} (\frac{x ^{4}}{8}) = \frac{x ^{3}}{2}

\frac{d}{d x} (\frac{32}{x ^{3}}) = - \frac{96}{x ^{4}}

= \frac{x ^{3}}{2} - (- \frac{96}{x ^{4}})

Vereinfache

= \frac{x ^{3}}{2} + \frac{96}{x ^{4}}

\int_{- 4 π}^{4 π} (sin^{2} (x) + 1) d x

a re a x^{3} - 11 x^{2} + 28 x, - x^{3} + 11 x^{2} - 28 x

y^{^{'}} = e^{x^{2}}

\frac{d}{d x} (e^{l n (l n (2 x))})

x \to 2 lim (\frac{4}{( x - 2 ) ^{2}})