derivative f(x)=3x^3(x^2-2)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 3 (5 x^{4} - 6 x^{2})

d er i v a t i v e f (x) = (3 x^{2} - 2) (5 x + 5)

\int \frac{1}{1 - cos ^{2} ( x )} d x

d er i v a t i v e 7 t + 6 t^{7}

a re a y = 5 x - x^{2}, y = - x

\frac{\partial}{\partial x} (3 y cos (x))