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

Lösung

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

e^{x y} x y^{2} + 2 y e^{x y} - \frac{x}{y ^{2}}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= e^{x y} x y^{2} + 2 y e^{x y} - \frac{x}{y ^{2}}

\frac{\partial}{\partial r} (r^{2} + s^{2})

\frac{d}{d x} (sin (x))

d er i v a t i v e y = (7 - 3 x^{3})^{3}

\int 16 e^{x} d x

d er i v a t i v e \frac{f ( x )}{x ^{2} + 8}