(\partial)/(\partial y)((z)(x^2+3xy+y^2))

Lösung

\frac{\partial}{\partial y} ((z) (x^{2} + 3 x y + y^{2}))

z (3 x + 2 y)

Schritte zur Lösung

\frac{\partial}{\partial y} ((z) (x^{2} + 3 x y + y^{2}))

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= z \frac{\partial}{\partial y} (x^{2} + 3 x y + y^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (\frac{\partial}{\partial y} (x^{2}) + \frac{\partial}{\partial y} (3 x y) + \frac{\partial}{\partial y} (y^{2}))

\frac{\partial}{\partial y} (x^{2}) = 0

\frac{\partial}{\partial y} (3 x y) = 3 x

\frac{\partial}{\partial y} (y^{2}) = 2 y

= z (0 + 3 x + 2 y)

Vereinfache

= z (3 x + 2 y)

e x p an d (a e - b d)^{2} + (a f - c d)^{2} + (b f - ce)^{2}

e x p an d (A + B = 2,) (- 2 A + C = 3)

e x p an d \frac{5 ( 3 b ^{2} + 4 b - 6 )}{4}

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

s im pl i f y (x - 13)^{2}