derivative of (x3x(x+4)^2)

Lösung

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

3 (4 x^{3} + 24 x^{2} + 32 x)

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = (x + 4)^{2}

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

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

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

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

Multipliziere aus

2 x (x + 4)^{2} + 2 (x + 4) x^{2} : 4 x^{3} + 24 x^{2} + 32 x

= 3 (4 x^{3} + 24 x^{2} + 32 x)

e x p an d \frac{2 ( s + 2 )}{s ^{2} + 4 s + 3}

e x p an d - \frac{4}{( x + 1 ) ^{2}}

e x p an d 2 x e^{x} + e^{x} (x^{2} - 1)

e x p an d 90 - 12

e x p an d x ((- b x) - 1)