derivative of (x^2+3(x^2-3)x^2)

Lösung

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

6 x^{5} - 18 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x (x^{2} - 3) x^{2} + (4 x^{3} - 6 x) (x^{2} + 3) : 6 x^{5} - 18 x

= 6 x^{5} - 18 x

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

g^{'} (x)

\int - \frac{6}{x} d x

x \to 0 - lim (arctan (\frac{1}{x}))

\frac{\partial}{\partial x} (x^{2} + 4 y)