derivative of \sqrt[3]{x}(x^2+4)

Lösung

\frac{d}{d x} (3 x (x^{2} + 4))

\frac{x ^{2} + 4 + 6 3 x x ^{\frac{5}{3}}}{3 x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (3 x (x^{2} + 4))

Wende die Produktregel an:

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

f = 3 x, g = x^{2} + 4

= \frac{d}{d x} (3 x) (x^{2} + 4) + \frac{d}{d x} (x^{2} + 4) 3 x

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

\frac{d}{d x} (x^{2} + 4) = 2 x

= \frac{1}{3 x ^{\frac{2}{3}}} (x^{2} + 4) + 2 x 3 x

Vereinfache

\frac{1}{3 x ^{\frac{2}{3}}} (x^{2} + 4) + 2 x 3 x : \frac{x ^{2} + 4 + 6 3 x x ^{\frac{5}{3}}}{3 x ^{\frac{2}{3}}}

= \frac{x ^{2} + 4 + 6 3 x x ^{\frac{5}{3}}}{3 x ^{\frac{2}{3}}}

\int e^{- v} d v

s l o p e (2, 3), (4, - 4)

t a y l or x \cdot e^{- x + 1}, 1

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

\int (5 e^{x}) d x