(\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 (4 x + 3)^{9} d x

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\int 7 sin^{4} (x) d x

\frac{d}{d x} (ln (x) cos (t))

\frac{d}{d x} (cot (e^{2 x}))