(\partial)/(\partial y)(xe^{xy})

Lösung

\frac{\partial}{\partial y} (x \cdot e^{x \cdot y})

e^{x y} x^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= x e^{x y} x

Vereinfache

x e^{x y} x : e^{x y} x^{2}

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

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

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x}

x \to 0 + lim ((ln (x))^{2})

d er i v a t i v e sec^{2} (x) + tan^{2} (x)

t an g e n t f (x) = 15 x - 1.86 x^{2}, at x = a