(\partial)/(\partial x)(xe^y-ye^x)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\int_{0}^{1} \frac{3 ^{3 x} - 1}{3 ^{x}} d x

d er i v a t i v e y = (2 x + 1) + \frac{2}{( 2 x + 1 ) ^{3}}

\int_{- 1}^{1} x (1 - x)^{2} d x

x \to 0 + lim (\frac{1}{sin ^{2} ( x )})

\frac{d}{d x} (\frac{24 x ( x ^{2} + 1 )}{( 1 - x ^{2} ) ^{4}})