d/(dt)((x)200(30-t^2))

Lösung

\frac{d}{d t} ((x) 200 (30 - t^{2}))

200 (\frac{d x}{d t} (30 - t^{2}) - 2 t x)

Schritte zur Lösung

\frac{d}{d t} ((x) \cdot 200 (30 - t^{2}))

Entferne die Konstante:

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

= 200 \frac{d}{d t} (x (30 - t^{2}))

Wende die Produktregel an:

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

f = x, g = 30 - t^{2}

= 200 (\frac{d x}{d t} (30 - t^{2}) + \frac{d}{d t} (30 - t^{2}) x)

\frac{d}{d t} (30 - t^{2}) = - 2 t

= 200 (\frac{d x}{d t} (30 - t^{2}) + (- 2 t) x)

Vereinfache

= 200 (\frac{d x}{d t} (30 - t^{2}) - 2 t x)

e x p an d \frac{x y ( x ^{2} - y ^{2} )}{x ^{2} + y ^{2}}

e x p an d (1 + 2)^{6}

e x p an d (\frac{4}{3} - x)^{2}

e x p an d (t - b) e^{a t}

e x p an d (x - 1)^{2} (x^{2} - 2 x + 1)