derivative f(x)=6x^2(x-9)

Lösung

ableitung von

f (x) = 6 x^{2} (x - 9)

6 (3 x^{2} - 18 x)

Schritte zur Lösung

\frac{d}{d x} (6 x^{2} (x - 9))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{2} (x - 9))

Wende die Produktregel an:

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

f = x^{2}, g = x - 9

= 6 (\frac{d}{d x} (x^{2}) (x - 9) + \frac{d}{d x} (x - 9) x^{2})

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

\frac{d}{d x} (x - 9) = 1

= 6 (2 x (x - 9) + 1 \cdot x^{2})

Vereinfache

6 (2 x (x - 9) + 1 \cdot x^{2}) : 6 (3 x^{2} - 18 x)

= 6 (3 x^{2} - 18 x)

\frac{\partial}{\partial x} (\frac{2}{x ^{3}})

\int \frac{4 x ^{2} - 9}{x} d x

x \to 2 lim (\frac{x ^{2} - 4}{2 - x})

\int e^{x} + 9 x d x

\frac{d}{d x} ((x - a)^{2})