derivative x^2(240-x/3)

Lösung

ableitung von

x^{2} (240 - \frac{x}{3})

480 x - x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} (240 - \frac{x}{3}))

Wende die Produktregel an:

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

f = x^{2}, g = 240 - \frac{x}{3}

= \frac{d}{d x} (x^{2}) (240 - \frac{x}{3}) + \frac{d}{d x} (240 - \frac{x}{3}) x^{2}

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

\frac{d}{d x} (240 - \frac{x}{3}) = - \frac{1}{3}

= 2 x (240 - \frac{x}{3}) + (- \frac{1}{3}) x^{2}

Vereinfache

2 x (240 - \frac{x}{3}) + (- \frac{1}{3}) x^{2} : 480 x - x^{2}

= 480 x - x^{2}

t an g e n t \frac{1}{2} x^{4} - 8

x y \frac{d y}{d x} + 4 x^{2} + y^{2} = 0

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

a re a x = y^{2} - 4 y, x = 2 y - y^{2}

\int \frac{1}{t ^{2} 400 - t ^{2}} d t