(\partial)/(\partial x)((z)(3x^2y+4xy^2))

Lösung

\frac{\partial}{\partial x} ((z) (3 x^{2} y + 4 x y^{2}))

z (6 y x + 4 y^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} ((z) (3 x^{2} y + 4 x y^{2}))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

= z \frac{\partial}{\partial x} (3 x^{2} y + 4 x y^{2})

Wende die Summen-/Differenzregel an:

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

= z (\frac{\partial}{\partial x} (3 x^{2} y) + \frac{\partial}{\partial x} (4 x y^{2}))

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

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

= z (6 y x + 4 y^{2})

e x p an d 6 (11 + 5)

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

e x p an d (t + a)^{2} + e^{- a t} - 2 cos (a t)

e x p an d \frac{1 + 2 ^{n}}{3 ^{n - 1}}

e x p an d \frac{3 x ^{2} - 10 x - 5}{( x - 1 ) ^{2} ( x + 2 )}