derivative of x(2x+9^{1/3})

Lösung

\frac{d}{d x} (x (2 x + 9)^{\frac{1}{3}})

\frac{8 x + 27}{3 ( 2 x + 9 ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (x (2 x + 9)^{\frac{1}{3}})

Wende die Produktregel an:

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

f = x, g = (2 x + 9)^{\frac{1}{3}}

= \frac{d x}{d x} (2 x + 9)^{\frac{1}{3}} + \frac{d}{d x} ((2 x + 9)^{\frac{1}{3}}) x

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

\frac{d}{d x} ((2 x + 9)^{\frac{1}{3}}) = \frac{2}{3 ( 2 x + 9 ) ^{\frac{2}{3}}}

= 1 \cdot (2 x + 9)^{\frac{1}{3}} + \frac{2}{3 ( 2 x + 9 ) ^{\frac{2}{3}}} x

Vereinfache

1 \cdot (2 x + 9)^{\frac{1}{3}} + \frac{2}{3 ( 2 x + 9 ) ^{\frac{2}{3}}} x : \frac{8 x + 27}{3 ( 2 x + 9 ) ^{\frac{2}{3}}}

= \frac{8 x + 27}{3 ( 2 x + 9 ) ^{\frac{2}{3}}}

\int_{0}^{\infty} t e^{- k t} d t

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

\frac{d}{d x} (2 x^{2} - 4)

\frac{d}{d x} (ln x^{2} - 4)

d er i v a t i v e f (x) = - 2 x^{2} - 12 x - 4