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

Lösung

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

5 x^{4} - 24 x^{3} + 27 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

3 x^{2} (x - 3)^{2} + 2 (x - 3) x^{3} : 5 x^{4} - 24 x^{3} + 27 x^{2}

= 5 x^{4} - 24 x^{3} + 27 x^{2}

x \to 0 lim (2)

\frac{d}{d x} (\frac{1}{3} x^{3} + 2 x - 4)

n = 0 \sum \infty (\frac{6}{5})^{n}

t an g e n t f (x) = x^{3} - x

\int 4 t^{3} cos (t^{4} + 1) d t