d/(dt)(({z}(t,x,y))(sqrt(1+x^2+y^2)))

Lösung

\frac{d}{d t} ((z (t, x, y)) (1 + x^{2} + y^{2}))

\frac{d}{d t} (z (t, x, y)) 1 + x^{2} + y^{2} + \frac{x \frac{d x}{d t} + y \frac{d y}{d t}}{1 + x ^{2} + y ^{2}} z (t, x, y)

Schritte zur Lösung

\frac{d}{d t} ((z (t, x, y)) (1 + x^{2} + y^{2}))

Wende die Produktregel an:

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

f = z (t, x, y), g = 1 + x^{2} + y^{2}

= \frac{d}{d t} (z (t, x, y)) 1 + x^{2} + y^{2} + \frac{d}{d t} (1 + x^{2} + y^{2}) z (t, x, y)

\frac{d}{d t} (1 + x^{2} + y^{2}) = \frac{x \frac{d x}{d t} + y \frac{d y}{d t}}{1 + x ^{2} + y ^{2}}

= \frac{d}{d t} (z (t, x, y)) 1 + x^{2} + y^{2} + \frac{x \frac{d x}{d t} + y \frac{d y}{d t}}{1 + x ^{2} + y ^{2}} z (t, x, y)

s im pl i f y x (x^{3} + 5)

e x p an d (x + 4 y)^{4}

s im pl i f y (1 + cot^{2} (x)) (1 - sin^{2} (x))

s im pl i f y \frac{150}{360}

s im pl i f y 5.68 \cdot 1 0^{26}