(\partial)/(\partial y)((z)(3x+5y)^9)

Lösung

\frac{\partial}{\partial y} ((z) (3 x + 5 y)^{9})

45 z (3 x + 5 y)^{8}

Schritte zur Lösung

\frac{\partial}{\partial y} ((z) (3 x + 5 y)^{9})

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= z \frac{\partial}{\partial y} ((3 x + 5 y)^{9})

Wende die Kettenregel an:

9 (3 x + 5 y)^{8} \frac{\partial}{\partial y} (3 x + 5 y)

= 9 (3 x + 5 y)^{8} \frac{\partial}{\partial y} (3 x + 5 y)

\frac{\partial}{\partial y} (3 x + 5 y) = 5

= z \cdot 9 (3 x + 5 y)^{8} \cdot 5

Vereinfache

= 45 z (3 x + 5 y)^{8}

e x p an d \frac{36 - 57 x + 15 x ^{2} - x ^{3}}{x ( 6 - x ) ^{2}}

e x p an d (x - 3 - 2 i) (x - 3 + 2 i)

e x p an d, 900 q - 10 w - 10 q (45 - \frac{1}{2} q)

e x p an d (x 3 + 2 x)^{2}

e x p an d \frac{12 ( - 6 x ^{2} + 7 )}{( 6 x ^{2} + 7 ) ^{2}}