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

Lösung

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

\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}}}

y^{^{''}} + 25 y = 2 sec (5 t)

x \to 0 lim (5^{x})

n = 6 \sum \infty e^{3 - 4 n}

x \to \infty lim (4 x - x^{2})

\frac{\partial}{\partial y} (x^{\frac{3}{2}} - 3 y)