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

Lösung

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

z (2 y - 3 x)

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 (2 y - 3 x)

e x p an d \frac{d}{d x} ((8 x + 3) (x^{2} - 1)) + \frac{x + 4}{5}

e x p an d (A x^{2} + B x + C) e^{3 x}

e x p an d \frac{( 2 x ^{3} - 3 ) ^{6}}{36 x ^{2}}

e x p an d f (t + 2 π)

e x p an d \frac{7 \cdot 2 ^{k + 1} + ( - 1 ) ^{k + 2}}{3}