derivative x(7x+1)^{1/3}

Lösung

ableitung von

x (7 x + 1)^{\frac{1}{3}}

\frac{28 x + 3}{3 ( 7 x + 1 ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (x (7 x + 1)^{\frac{1}{3}})

Wende die Produktregel an:

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

f = x, g = (7 x + 1)^{\frac{1}{3}}

= \frac{d x}{d x} (7 x + 1)^{\frac{1}{3}} + \frac{d}{d x} ((7 x + 1)^{\frac{1}{3}}) x

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

\frac{d}{d x} ((7 x + 1)^{\frac{1}{3}}) = \frac{7}{3 ( 7 x + 1 ) ^{\frac{2}{3}}}

= 1 \cdot (7 x + 1)^{\frac{1}{3}} + \frac{7}{3 ( 7 x + 1 ) ^{\frac{2}{3}}} x

Vereinfache

1 \cdot (7 x + 1)^{\frac{1}{3}} + \frac{7}{3 ( 7 x + 1 ) ^{\frac{2}{3}}} x : \frac{28 x + 3}{3 ( 7 x + 1 ) ^{\frac{2}{3}}}

= \frac{28 x + 3}{3 ( 7 x + 1 ) ^{\frac{2}{3}}}

t an g e n t 5 x^{3} - 5 x

d er i v a t i v e f (x) = \frac{x ^{2}}{3}

\int \frac{( arctan ( x ) )}{x ^{2}} d x

\int_{0}^{1} 39 \frac{1}{x ^{p}} d x

d er i v a t i v e ln (1 - x)