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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{5 x + 6}{6 x ^{\frac{2}{3}}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 3 x, g = x + 3

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

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

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

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

Vereinfache

\frac{1}{3 x ^{\frac{2}{3}}} (x + 3) + \frac{1}{2 x} 3 x : \frac{5 x + 6}{6 x ^{\frac{2}{3}}}

= \frac{5 x + 6}{6 x ^{\frac{2}{3}}}

Graph

Beliebte Beispiele

integral from 1 to 2 of 1/x-x

\int_{1}^{2} \frac{1}{x} - x d x

integral of cot(y)

\int cot (y) d y

limit as x approaches 0+of x(1-cos(1/x))

x \to 0 + lim (x (1 - cos (\frac{1}{x})))

integral of 1/(x^2*sqrt(x^2+4))

\int \frac{1}{x ^{2} \cdot x ^{2} + 4} d x

(dx)/(dt)-5x=sin(2t),x(0)=pi

\frac{d x}{d t} - 5 x = sin (2 t), x (0) = π