(\partial)/(\partial y)(2xe^{x^2-y^2})

Lösung

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

- 4 e^{x^{2} - y^{2}} x y

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

= - 4 e^{x^{2} - y^{2}} x y

\int y e^{- y} d y

\frac{d}{d x} (cos^{2} (sin (4 x)))

y^{^{''}} + 5 y^{^{'}} + 6 y = 2 e^{x}, y (0) = 1, y^{^{'}} (0) = - 1

\int 4 sin (5 x) + 5 cos (3 x) d x

\frac{d y}{d t} = 2 y - t