derivative of x(x-1^3)

Lösung

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

(x - 1)^{3} + 3 x (x - 1)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = (x - 1)^{3}

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

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

\frac{d}{d x} ((x - 1)^{3}) = 3 (x - 1)^{2}

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

Vereinfache

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

\int - x^{2} (x + 1)^{3} (x - 1) d x

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

\int_{0}^{3} (- x^{2} + x - 1) d x

\int_{1}^{16} \frac{1}{x} d x

\int \frac{2 x}{3 ( x ^{2} + 1 )} d x