derivative of x(x-3^2)

Lösung

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

3 x^{2} - 12 x + 9

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

1 \cdot (x - 3)^{2} + 2 (x - 3) x : 3 x^{2} - 12 x + 9

= 3 x^{2} - 12 x + 9

a re a y = x^{2}, y = - x^{2} + 4 x

\int 12 sin^{6} (x) cos^{3} (x) d x

d er i v a t i v e f (x) = x^{\frac{5}{11}} (x - 5)^{2}

\frac{\partial}{\partial x} (\frac{3 x + 2 y}{y ^{2} + 5 x ^{2}})

\int 3 + 4 x d x