(\partial)/(\partial y)(1/y e^{xy})

Lösung

\frac{\partial}{\partial y} (\frac{1}{y} e^{x y})

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

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{1}{y} e^{x y})

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{y}, g = e^{x y}

= \frac{\partial}{\partial y} (\frac{1}{y}) e^{x y} + \frac{\partial}{\partial y} (e^{x y}) \frac{1}{y}

\frac{\partial}{\partial y} (\frac{1}{y}) = - \frac{1}{y ^{2}}

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

= (- \frac{1}{y ^{2}}) e^{x y} + e^{x y} x \frac{1}{y}

Vereinfache

(- \frac{1}{y ^{2}}) e^{x y} + e^{x y} x \frac{1}{y} : - \frac{e ^{y x}}{y ^{2}} + \frac{e ^{y x} x}{y}

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

\int_{1}^{13} \frac{x - 1}{72} d x

s l o p e in t erce pt (- 1, 1), (1, 0)

\frac{d}{d x} (\frac{2}{cos ( 7 x )})

t an g e n t f (x) = x^{4}

t an g e n t y = x + \frac{2}{x}, (2, 3)