erweitern z(u,v,w(z,u,v))(2u+v-w(z,u,v)+3z(u,v,w(z,u,v))=0)

Lösung

erweitern

z (u, v, w (z, u, v)) (2 u + v - w (z, u, v) + 3 z (u, v, w (z, u, v)) = 0)

2 z u (,, uv w (,, z uv)) + z v (,, uv w (,, z uv)) - z (,, uv w (,, z uv)) w (,, z uv) + 3 zz (,, uv w (,, z uv)) (,, uv w (,, z uv)) = 0

Schritte zur Lösung

z (u, v, w (z, u, v)) (2 u + v - w (z, u, v) + 3 z (u, v, w (z, u, v)) = 0)

= z (,, uv w (,, z uv)) (2 u + v - w (,, z uv) + 3 \cdot 0 = z (,, uv w (,, z uv)))

Setze Klammern

z (u, v, w (z, u, v)) \cdot 2 u + z (u, v, w (z, u, v)) v + z (u, v, w (z, u, v)) (- w (z, u, v)) + z (u, v, w (z, u, v)) \cdot 3 z (u, v, w (z, u, v)) = 0

Wende Minus-Plus Regeln an

+ (- a) = - a

2 z u (,, uv w (,, z uv)) + z v (,, uv w (,, z uv)) - z (,, uv w (,, z uv)) w (,, z uv) + 3 zz (,, uv w (,, z uv)) (,, uv w (,, z uv)) = 0

e x p an d 126 + 32

e x p an d - \frac{4 ( - 2 x ^{2} + 5 )}{7 x - 9}

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

e x p an d 4 (4 X^{3} + 2 X^{2} - 5 X)^{2}

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