derivative x(5x+3)^{1/3}

Lösung

ableitung von

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

\frac{20 x + 9}{3 ( 5 x + 3 ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (x (5 x + 3)^{\frac{1}{3}})

Wende die Produktregel an:

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

f = x, g = (5 x + 3)^{\frac{1}{3}}

= \frac{d x}{d x} (5 x + 3)^{\frac{1}{3}} + \frac{d}{d x} ((5 x + 3)^{\frac{1}{3}}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((5 x + 3)^{\frac{1}{3}}) = \frac{5}{3 ( 5 x + 3 ) ^{\frac{2}{3}}}

= 1 \cdot (5 x + 3)^{\frac{1}{3}} + \frac{5}{3 ( 5 x + 3 ) ^{\frac{2}{3}}} x

Vereinfache

1 \cdot (5 x + 3)^{\frac{1}{3}} + \frac{5}{3 ( 5 x + 3 ) ^{\frac{2}{3}}} x : \frac{20 x + 9}{3 ( 5 x + 3 ) ^{\frac{2}{3}}}

= \frac{20 x + 9}{3 ( 5 x + 3 ) ^{\frac{2}{3}}}

\int 8 (x + 1) I n (x + 1) d x

n = 0 \sum \infty z^{3 n}

x \to \infty lim (\frac{a _{n + 1}}{a _{n}})

\frac{d r}{d t} = \frac{1}{t + 1}, r (0) = 1

(1 + x^{2}) y^{^{'}} + 1 + 2 x y = 0