(\partial)/(\partial y)(2(y+4)^3(x-5))

Lösung

\frac{\partial}{\partial y} (2 (y + 4)^{3} (x - 5))

6 (x - 5) (y + 4)^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (2 (y + 4)^{3} (x - 5))

Behandle

x

als Konstante

Entferne die Konstante:

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

= 2 (x - 5) \frac{\partial}{\partial y} ((y + 4)^{3})

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (y + 4) = 1

= 2 (x - 5) \cdot 3 (y + 4)^{2} \cdot 1

Vereinfache

= 6 (x - 5) (y + 4)^{2}

x \to - 1 lim (7 x - 2 x^{2})

d er i v a t i v e y = 1 + 2 x

y^{^{''}} + 12 y^{^{'}} + 117 y = 0

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

d er i v a t i v e y = 2 - x