(\partial)/(\partial z)((e^{xz+y})/(z^2+w))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x, y, w

als Konstanten

Wende die Quotientenregel an:

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

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

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

\frac{\partial}{\partial z} (z^{2} + w) = 2 z

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

\int 25 - x^{2} (2 x) d x

\int_{2}^{5} e^{4 x} d x

\int \frac{t}{9 + t ^{2}} d t

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

\frac{d}{d x} (sin (\frac{π x}{8}))