(\partial)/(\partial x)(2x^4y-3xy+9y)

Lösung

\frac{\partial}{\partial x} (2 x^{4} y - 3 x y + 9 y)

8 x^{3} y - 3 y

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x^{4} y - 3 x y + 9 y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2 x^{4} y) - \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (9 y)

\frac{\partial}{\partial x} (2 x^{4} y) = 8 y x^{3}

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

\frac{\partial}{\partial x} (9 y) = 0

= 8 y x^{3} - 3 y + 0

Vereinfache

= 8 x^{3} y - 3 y

\frac{d y}{d x} = 3 x + y - 3

\int_{0}^{10} x e^{- 0.6 x} d x

\frac{\partial}{\partial y} (y (2 - x - y))

\int x (x^{2} + 1) d x

x y^{^{'}} - y^{^{'}} - (x - 1) sin (x) + y = 0