d/(dt)((x)(kx(t)^2))

Lösung

\frac{d}{d t} ((x (t)) (k x (t) (t)^{2}))

k (2 t x (t)^{2} + 2 x (t) \frac{d}{d t} (x (t)) t^{2})

Schritte zur Lösung

\frac{d}{d t} ((x (t)) (k x (t) (t)^{2}))

Vereinfache

(x (t)) (k x (t) (t)^{2}) : k t^{2} x (t)^{2}

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = t^{2}, g = x (t)^{2}

= k (\frac{d}{d t} (t^{2}) x (t)^{2} + \frac{d}{d t} (x (t)^{2}) t^{2})

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

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

= k (2 t x (t)^{2} + 2 x (t) \frac{d}{d t} (x (t)) t^{2})

f (x) = 191.7 x^{432}

f a c t or F e (N O^{3}) 3

s im pl i f y 9000 (1.00048)^{35}

\frac{d}{d w} ((z) (e^{z w}))

f (x) = (sin (3 x))^{4}