derivative of 2sqrt(x)+1/(3x^3)

Lösung

\frac{d}{d x} (2 x + \frac{1}{3 x ^{3}})

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

Schritte zur Lösung

\frac{d}{d x} (2 x + \frac{1}{3 x ^{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x) + \frac{d}{d x} (\frac{1}{3 x ^{3}})

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

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

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

Vereinfache

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

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

t a y l or x + \frac{x ^{3}}{3} - tan (x)

x \to \infty lim (\frac{( e ^{x} + e ^{- x} )}{2})

\frac{d}{d x} (x^{2} arctan (2 x))

\frac{d}{d x} (4 sin (x) - 4 x cos (x))

n = 3 \sum \infty \frac{1}{n ^{2} + 3 n}