(\partial)/(\partial x)(x/(x+y)+e^{xy}x+4y)

Lösung

\frac{\partial}{\partial x} (\frac{x}{x + y} + e^{x y} x + 4 y)

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{x + y} + e^{x y} x + 4 y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (\frac{x}{x + y}) + \frac{\partial}{\partial x} (e^{x y} x) + \frac{\partial}{\partial x} (4 y)

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

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

\frac{\partial}{\partial x} (4 y) = 0

= \frac{y}{( x + y ) ^{2}} + y e^{y x} x + e^{y x} + 0

Vereinfache

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

\frac{d}{d x} (\frac{x - x ^{2}}{x})

\frac{d}{d x} (2 cos (\frac{x}{2}))

d er i v a t i v e - 4 (x - 9)^{3}

t a y l or (sin (x)), \frac{π}{2}

n = 1 \sum \infty \frac{2 n}{3 n}