derivative of 3x^{1/3}+2x^2

Lösung

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

\frac{1 + 4 x ^{\frac{5}{3}}}{x ^{\frac{2}{3}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

\frac{1}{x ^{\frac{2}{3}}} + 4 x : \frac{1 + 4 x ^{\frac{5}{3}}}{x ^{\frac{2}{3}}}

= \frac{1 + 4 x ^{\frac{5}{3}}}{x ^{\frac{2}{3}}}

\int e^{3 x} sin (e^{x}) d x

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

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

n \to \infty lim (\frac{( - 1 ) ^{n + 1}}{( n + 3 ) \cdot n !})

\int x^{3} x^{2} - 8 d x