(\partial)/(\partial y)(e^{xy}+2x+3y)

Lösung

\frac{\partial}{\partial y} (e^{x y} + 2 x + 3 y)

e^{x y} x + 3

Schritte zur Lösung

\frac{\partial}{\partial y} (e^{x y} + 2 x + 3 y)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (e^{x y}) + \frac{\partial}{\partial y} (2 x) + \frac{\partial}{\partial y} (3 y)

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

\frac{\partial}{\partial y} (2 x) = 0

\frac{\partial}{\partial y} (3 y) = 3

= e^{x y} x + 0 + 3

Vereinfache

= e^{x y} x + 3

\int 3 e^{8 x} d x

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

\int \frac{1}{7 x ( 1 + 7 x )} d x

\frac{d}{d x} (\frac{1}{g ( x ) ( x ) ^{2} ( x )})

\int \frac{( 4 x - 3 )}{x + 1} d x