(\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 sin (a) (1 - cos (b)) + sin (b) (1 - cos (a))

e x p an d 2 (3 + 5)

e x p an d 4 (\frac{1}{2} x + \frac{3}{2} y)

e x p an d lo g_{10} (x y z)

e x p an d (x^{2} + y^{2} + z^{2})^{4}