(\partial)/(\partial x)((e^x)/(y+x^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

x \to 2 lim (\frac{4}{x - 2})

t \to 0 lim (e^{- 2 t})

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

n = 1 \sum \infty ln (\frac{n}{3 n + 1})

\int \frac{3}{x ^{- 1} + 3} d x