(\partial)/(\partial y)(8cos(ye^{xy})sin(x))

Lösung

\frac{\partial}{\partial y} (8 cos (y e^{x y}) sin (x))

- 8 sin (e^{y x} y) sin (x) (e^{y x} + e^{y x} y x)

Schritte zur Lösung

\frac{\partial}{\partial y} (8 cos (y e^{x y}) sin (x))

Behandle

x

als Konstante

Entferne die Konstante:

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

= 8 sin (x) \frac{\partial}{\partial y} (cos (y e^{x y}))

Wende die Kettenregel an:

- sin (y e^{x y}) \frac{\partial}{\partial y} (y e^{x y})

= - sin (y e^{x y}) \frac{\partial}{\partial y} (y e^{x y})

\frac{\partial}{\partial y} (y e^{x y}) = e^{x y} + x e^{x y} y

= 8 sin (x) (- sin (y e^{x y}) (e^{x y} + x e^{x y} y))

Vereinfache

= - 8 sin (e^{y x} y) sin (x) (e^{y x} + e^{y x} y x)

\int (sin (θ))^{3} d θ

d er i v a t i v e 4 sec (x)

x \to - 9 - lim (\frac{1}{x - 9})

x \to 0 + lim (ln (0))

d er i v a t i v e y = 6 cos (x)