(\partial)/(\partial x)((z)(xz+xyz-5))

Lösung

\frac{\partial}{\partial x} ((z) (x z + x yz - 5))

z (z + zy)

Schritte zur Lösung

\frac{\partial}{\partial x} ((z) (x z + x yz - 5))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

= z \frac{\partial}{\partial x} (x z + x yz - 5)

Wende die Summen-/Differenzregel an:

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

= z (\frac{\partial}{\partial x} (x z) + \frac{\partial}{\partial x} (x yz) - \frac{\partial}{\partial x} (5))

\frac{\partial}{\partial x} (x z) = z

\frac{\partial}{\partial x} (x yz) = zy

\frac{\partial}{\partial x} (5) = 0

= z (z + zy - 0)

Vereinfache

= z (z + zy)

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

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

e x p an d \frac{( 4 x - 1 ) ^{4}}{16}

s im pl i f y \frac{1}{2} (u - \frac{1}{2} sin (2 u))

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