derivative of x^2(6-x^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = (6 - x)^{3}

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

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

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

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

Vereinfache

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

\int \frac{1}{x ^{2} + 8 x + 20} d x

x \to 0 lim (\frac{4}{x} - \frac{4}{∣ x ∣})

y^{^{'}} + y = 5 sin (2 x)

\frac{\partial}{\partial x} (sin (n x) e^{- n^{2} t})

x \to \infty lim (1 - e^{x})