derivative of x^{2/3}(5-x)

Lösung

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

\frac{10 - 5 x}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (5 - x) = - 1

= \frac{2}{3 x ^{\frac{1}{3}}} (5 - x) + (- 1) x^{\frac{2}{3}}

Vereinfache

\frac{2}{3 x ^{\frac{1}{3}}} (5 - x) + (- 1) x^{\frac{2}{3}} : \frac{10 - 5 x}{3 x ^{\frac{1}{3}}}

= \frac{10 - 5 x}{3 x ^{\frac{1}{3}}}

a re a 19 - x^{2}, - 2 x + 16, - 5, - 19

\frac{\partial}{\partial x} (y \cdot ∣ x ∣)

(x^{2} + 1) y^{^{'}} + 9 x (y - 1) = 0, y (0) = 2

\frac{d P}{d t} - a P = b

d x + e^{9 x} d y = 0