derivative of x/3 (2x+1^3)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((2 x + 1)^{3}) = 6 (2 x + 1)^{2}

= \frac{1}{3} (1 \cdot (2 x + 1)^{3} + 6 (2 x + 1)^{2} x)

Vereinfache

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

= \frac{( 2 x + 1 ) ^{3} + 6 x ( 2 x + 1 ) ^{2}}{3}

d er i v a t i v e g (x) = ln (x e^{- 7 x})

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

x \to 0 lim (\frac{ln ( \frac{1 + x}{1 - x} ) - 2 x}{x - sin ( x )})

d er i v a t i v e f (t) = 80 t + t^{2} - \frac{1}{48} t^{3}

\int_{1}^{16} \frac{8}{x} d x