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Beliebt Rechnen >

derivative of \sqrt[3]{x^2}+5sqrt(x^3)

Lösung

\frac{d}{d x} (3 x^{2} + 5 x^{3})

Lösung

\frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

Schritte zur Lösung

\frac{d}{d x} (3 x^{2} + 5 x^{3})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (5 x^{3})

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

\frac{d}{d x} (5 x^{3}) = \frac{15 x}{2}

= \frac{2}{3 x ^{\frac{1}{3}}} + \frac{15 x}{2}

Vereinfache

\frac{2}{3 x ^{\frac{1}{3}}} + \frac{15 x}{2} : \frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

= \frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

Graph

Beliebte Beispiele

fläche sqrt(6x-x^2),0,6

a re a 6 x - x^{2}, 0, 6

0.5y^{''}+10y^'+100y=150,y(0)=0,y^'(0)=0

0.5 y^{^{''}} + 10 y^{^{'}} + 100 y = 150, y (0) = 0, y^{^{'}} (0) = 0

derivative f(x)=(3x+4)/(3x-4)

d er i v a t i v e f (x) = \frac{3 x + 4}{3 x - 4}

integral of (sin(2x))^3(cos(2x))^2

\int (sin (2 x))^{3} (cos (2 x))^{2} d x

integral of (1+x^2)e^{-x}

\int (1 + x^{2}) e^{- x} d x