(\partial)/(\partial y)((z)(xe^{yz}+ye^{xz}+3xyz-2))

Lösung

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

z (e^{zy} z x + 3 z x + e^{z x})

Schritte zur Lösung

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

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial y} (x e^{yz}) = x e^{yz} z

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

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

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

= z (x e^{yz} z + e^{z x} + 3 z x - 0)

Vereinfache

= z (e^{zy} z x + 3 z x + e^{z x})

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

e x p an d \frac{1}{( a - x ) ( b - x )}

s im pl i f y (cos (\frac{θ}{2}) + sin (\frac{θ}{2}) e^{i φ})^{2}

e x p an d e^{3 x y} \cdot 3 (y + x \frac{d y}{d x})

e x p an d 50 (24 - 23 e^{- \frac{t}{200}})