derivative of sqrt(x)+1/(x^3)

Lösung

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

\frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} - \frac{3}{x ^{4}}

Vereinfache

\frac{1}{2 x} - \frac{3}{x ^{4}} : \frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

= \frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

d er i v a t i v e (8 x^{2} - 5)^{\frac{1}{2}}

\int_{0}^{3} (2 x - 1) d x

d er i v a t i v e f (y) = 5 x + \frac{135}{x} (15 x + 30)

\int \frac{4 e ^{x}}{e ^{x} + 3} d x

f (x) = (e^{x} + 1)^{7 x}