derivative of bx^2(x-4)

Lösung

\frac{d}{d x} (b x^{2} (x - 4))

b (3 x^{2} - 8 x)

Schritte zur Lösung

\frac{d}{d x} (b x^{2} (x - 4))

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = x - 4

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

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

\frac{d}{d x} (x - 4) = 1

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

Vereinfache

b (2 x (x - 4) + 1 \cdot x^{2}) : b (3 x^{2} - 8 x)

= b (3 x^{2} - 8 x)

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

x \to 1 lim (10 x + 1)

\int x (x^{2} + 2)^{2} d x

in v erse l a pl a ce 4 (\frac{( 1 )}{s ^{2} + 16})

a re a y = \frac{2}{x}, y = 7 - x