derivative of (5x^3-2x^2(6x^3))

Lösung

\frac{d}{d x} ((5 x^{3} - 2 x^{2}) (6 x^{3}))

6 (30 x^{5} - 10 x^{4})

Schritte zur Lösung

\frac{d}{d x} ((5 x^{3} - 2 x^{2}) (6 x^{3}))

Entferne die Konstante:

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

= 6 \frac{d}{d x} ((5 x^{3} - 2 x^{2}) x^{3})

Wende die Produktregel an:

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

f = 5 x^{3} - 2 x^{2}, g = x^{3}

= 6 (\frac{d}{d x} (5 x^{3} - 2 x^{2}) x^{3} + \frac{d}{d x} (x^{3}) (5 x^{3} - 2 x^{2}))

\frac{d}{d x} (5 x^{3} - 2 x^{2}) = 15 x^{2} - 4 x

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

= 6 ((15 x^{2} - 4 x) x^{3} + 3 x^{2} (5 x^{3} - 2 x^{2}))

Multipliziere aus

(15 x^{2} - 4 x) x^{3} + 3 x^{2} (5 x^{3} - 2 x^{2}) : 30 x^{5} - 10 x^{4}

= 6 (30 x^{5} - 10 x^{4})

\frac{d}{d x} (1 - \frac{x ^{2}}{16})

l a pl a ce t r an s f or m 2 t^{2} - 3 t + 3

x \to \infty lim (5 x^{4})

in v erse l a pl a ce \frac{\frac{1}{s + 1} + \frac{3}{2}}{s + 2}

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e - 4 x, y (0) = - 6, y^{^{'}} (0) = 1