derivative f(x)=4x^{(2)}(x-3)

Lösung

ableitung von

f (x) = 4 x^{(2)} (x - 3)

4 (3 x^{2} - 6 x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = x - 3

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

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

\frac{d}{d x} (x - 3) = 1

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

Vereinfache

4 (2 x (x - 3) + 1 \cdot x^{2}) : 4 (3 x^{2} - 6 x)

= 4 (3 x^{2} - 6 x)

x \to \infty lim (x^{2} + 2 x)

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

\frac{\partial}{\partial y} (x^{3} y^{10} sin (x y^{2}))

\int 6 t e^{3 t} d t

x \to 0 lim (\frac{x ^{3}}{x ^{3}})