derivative f(x)=x^2(4-x)^2

Lösung

ableitung von

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

4 x^{3} - 24 x^{2} + 32 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 4 x^{3} - 24 x^{2} + 32 x

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

\int (2 x^{2} + 3 x - 5) sin (x) d x

t an g e n t f (x) = 3 x^{3} - x^{2} + 7, at x = 2

s l o p e 6 x - x^{2}

\int_{1}^{5} \frac{x}{x - 1} d x