(\partial)/(\partial y)((z)(6x^5+4y^3+4y))

Lösung

\frac{\partial}{\partial y} ((z) (6 x^{5} + 4 y^{3} + 4 y))

z (12 y^{2} + 4)

Schritte zur Lösung

\frac{\partial}{\partial y} ((z) (6 x^{5} + 4 y^{3} + 4 y))

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= z \frac{\partial}{\partial y} (6 x^{5} + 4 y^{3} + 4 y)

Wende die Summen-/Differenzregel an:

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

= z (\frac{\partial}{\partial y} (6 x^{5}) + \frac{\partial}{\partial y} (4 y^{3}) + \frac{\partial}{\partial y} (4 y))

\frac{\partial}{\partial y} (6 x^{5}) = 0

\frac{\partial}{\partial y} (4 y^{3}) = 12 y^{2}

\frac{\partial}{\partial y} (4 y) = 4

= z (0 + 12 y^{2} + 4)

Vereinfache

= z (12 y^{2} + 4)

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

e x p an d (3 x + 2 y - 2) d x + (6 x + 4 y + 4) d y

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

e x p an d lo g_{7} (3 3^{5})

e x p an d - 5 (4 + 2)