(\partial)/(\partial x)((z)(x^4y+xz+yz^2))

Lösung

\frac{\partial}{\partial x} ((z) (x^{4} y + x z + y z^{2}))

z (z + 4 x^{3} y)

Schritte zur Lösung

\frac{\partial}{\partial x} ((z) (x^{4} y + x z + y z^{2}))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

= z \frac{\partial}{\partial x} (x^{4} y + x z + y z^{2})

Wende die Summen-/Differenzregel an:

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

= z (\frac{\partial}{\partial x} (x^{4} y) + \frac{\partial}{\partial x} (x z) + \frac{\partial}{\partial x} (y z^{2}))

\frac{\partial}{\partial x} (x^{4} y) = 4 y x^{3}

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

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

= z (4 y x^{3} + z + 0)

Vereinfache

= z (z + 4 x^{3} y)

e x p an d 2 (7 + 3)

e x p an d y cos (x y) (y + x (\frac{d y}{d x}))

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

e x p an d \frac{cos ( x ) + i sin ( x )}{( cos ( a ) - sin ( a ) i ) ^{2}}

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