derivative of 1/2 x^2\sqrt[3]{x}

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = 3 x

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

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

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

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

Vereinfache

\frac{1}{2} (2 x 3 x + \frac{1}{3 x ^{\frac{2}{3}}} x^{2}) : x 3 x + \frac{x ^{\frac{4}{3}}}{6}

= x 3 x + \frac{x ^{\frac{4}{3}}}{6}

d er i v a t i v e f (x) = 2 x + 3

in v erse l a pl a ce \frac{( s + 2 )}{( s ^{2} + 9 )}

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

a re a y = x^{3}, y = 2 x^{2}

\int 8 x^{3} - 9 x^{2} + 4 d x