derivative 2x(x+3)^2

Lösung

ableitung von

2 x (x + 3)^{2}

2 (3 x^{2} + 12 x + 9)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 (1 \cdot (x + 3)^{2} + 2 (x + 3) x) : 2 (3 x^{2} + 12 x + 9)

= 2 (3 x^{2} + 12 x + 9)

\frac{d}{d y} (\frac{2 y}{x ^{2} + y ^{2}})

\frac{d P}{d t} = P + a

a re a 5 - 4 x, \frac{1}{x}

y^{^{'}} - \frac{4}{x} y = \frac{y ^{3}}{x ^{5}}, y (1) = 1

s l o p e (1.1) (2.5)