(\partial)/(\partial x)(cos(xy)e^{y^2})

Lösung

\frac{\partial}{\partial x} (cos (x y) e^{y^{2}})

- e^{y^{2}} y sin (x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (cos (x y) e^{y^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= e^{y^{2}} \frac{\partial}{\partial x} (cos (x y))

Wende die Kettenregel an:

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

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

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

= e^{y^{2}} (- sin (x y) y)

Vereinfache

= - e^{y^{2}} y sin (x y)

\frac{d}{d x} (\frac{x ^{2} + 2 x - 3}{( x + 1 ) ^{2}})

d er i v a t i v e ln (22 x)

a re a x + 1 = y^{2}, y^{2} + 2 x = 10

12 y^{^{''}} + 5 y^{^{'}} - 3 y = 0

y^{^{'}} + \frac{4}{x} y = x^{4}