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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

= 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

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

Vereinfache

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

\int_{0}^{4} x 16 - x^{2} d x

\int \frac{1 - t}{t} d t

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 3

\frac{d}{d x} (3 sin^{2} (2 x))

\int sec (1) d x