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

Lösung

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

z (z^{3} + y)

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (x z^{3}) = z^{3}

\frac{\partial}{\partial x} (2 yz) = 0

= z (y + z^{3} - 0)

Vereinfache

= z (z^{3} + y)

e x p an d \frac{( x - 3 ) ( x + 4 )}{( x + 3 ) ( - x ^{3} + 9 x ^{2} - 25 x + 35 )}

e x p an d (2 x^{3} + 4 x^{2} - 5 x) l e f t (3 x y - 4 y)

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

e x p an d (cos (2 π t) - 2 π t \cdot sin (2 π t))^{2}

e x p an d \frac{d}{d v} ((p (v)) (p (v) + \frac{5.9}{v ^{2}})) + (v - 1.7)