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

Lösung

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

z (2 x - 3 y)

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= z (2 x - 3 y + 0)

Vereinfache

= z (2 x - 3 y)

e x p an d \frac{( n + 1 ) n}{2}

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

e x p an d \frac{1}{6} π (5, 5 + 2.5) + 2 (5.5 - 2.5)

e x p an d \frac{2}{( x + 1 ) ( x + 3 )}

e x p an d \frac{[ ( x + h ) + 5 ] ^{\frac{2}{3}} - ( x + 5 ) ^{\frac{2}{3}}}{h}