derivative of-0.0006x(x-15^2(x-40))

Lösung

\frac{d}{d x} (- 0.0006 x (x - 15)^{2} (x - 40))

- 0.0006 (4 x^{3} - 210 x^{2} + 2850 x - 9000)

Schritte zur Lösung

\frac{d}{d x} (- 0.0006 x (x - 15)^{2} (x - 40))

Entferne die Konstante:

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

= - 0.0006 \frac{d}{d x} (x (x - 15)^{2} (x - 40))

Wende die Produktregel an:

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

f = x, g = (x - 15)^{2} (x - 40)

= - 0.0006 (\frac{d x}{d x} (x - 15)^{2} (x - 40) + \frac{d}{d x} ((x - 15)^{2} (x - 40)) x)

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

\frac{d}{d x} ((x - 15)^{2} (x - 40)) = 3 x^{2} - 140 x + 1425

= - 0.0006 (1 \cdot (x - 15)^{2} (x - 40) + (3 x^{2} - 140 x + 1425) x)

Vereinfache

- 0.0006 (1 \cdot (x - 15)^{2} (x - 40) + (3 x^{2} - 140 x + 1425) x) : - 0.0006 (4 x^{3} - 210 x^{2} + 2850 x - 9000)

= - 0.0006 (4 x^{3} - 210 x^{2} + 2850 x - 9000)

d er i v a t i v e y = x (7 x + 3)^{\frac{1}{3}}

x \to + 0 lim (x^{3} cos (\frac{π}{x}))

\frac{\partial}{\partial x} (sin (2 x y))

\frac{d}{d x} (16 - \frac{1}{625} x^{2})

ma c l a u r in \frac{1}{4 - x}