d/(dt)(({z}(t,x,y))(6x^2+3xy(t)^2))

Lösung

\frac{d}{d t} ((z (t, x, y)) (6 x^{2} + 3 x y (t) (t)^{2}))

\frac{d}{d t} (z (t, x, y)) (6 x^{2} + 3 x y (t) t^{2}) + (12 x \frac{d x}{d t} + 3 (\frac{d x}{d t} y (t) t^{2} + (\frac{d}{d t} (y (t)) t^{2} + 2 t y (t)) x)) z (t, x, y)

Schritte zur Lösung

\frac{d}{d t} ((z (t, x, y)) (6 x^{2} + 3 x y (t) (t)^{2}))

Wende die Produktregel an:

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

f = z (t, x, y), g = 6 x^{2} + 3 x y (t) t^{2}

= \frac{d}{d t} (z (t, x, y)) (6 x^{2} + 3 x y (t) t^{2}) + \frac{d}{d t} (6 x^{2} + 3 x y (t) t^{2}) z (t, x, y)

\frac{d}{d t} (6 x^{2} + 3 x y (t) t^{2}) = 12 x \frac{d x}{d t} + 3 (\frac{d x}{d t} y (t) t^{2} + (\frac{d}{d t} (y (t)) t^{2} + 2 t y (t)) x)

= \frac{d}{d t} (z (t, x, y)) (6 x^{2} + 3 x y (t) t^{2}) + (12 x \frac{d x}{d t} + 3 (\frac{d x}{d t} y (t) t^{2} + (\frac{d}{d t} (y (t)) t^{2} + 2 t y (t)) x)) z (t, x, y)

e x p an d (x - (- 1 + i)) (x - (- 1 - i))

e x p an d ((X Y) + Z) \Rightarrow W

e x p an d x^{4} (e^{x} x - e^{x})

e x p an d \frac{2 ( 7 - 19 )}{3}

e x p an d - 2.4 + 0.7 - 11 - 5