derivative of 2x(x+4^3)

Lösung

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

2 ((x + 4)^{3} + 3 x (x + 4)^{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = (x + 4)^{3}

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

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

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

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

Vereinfache

= 2 ((x + 4)^{3} + 3 x (x + 4)^{2})

\int e^{- t} cos (t) d t

\frac{d}{d t} (\frac{1}{2} e^{- 4 t} cos (8 t))

\int x^{3} sin (5 x) d x

\int x \cdot sin (\frac{x}{2}) d x

t an g e n t 0.72 x^{3} - 4.8 x^{2} + 0.6 x + 7.6