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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Quotientenregel an:

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

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

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

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

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

t an g e n t \frac{6}{3 x ^{2}} - x, at x = 1

\frac{d y}{d x} = 17

\frac{\partial}{\partial x} (y cos (π x))

\int t^{6} ln (t) d t

d er i v a t i v e f (x) = (2 - 3 x)^{3}