(\partial)/(\partial x)(((yx)/(zw))^{1/2})

Lösung

\frac{\partial}{\partial x} ((\frac{y x}{z w})^{\frac{1}{2}})

\frac{y ^{\frac{1}{2}} ( z w ) ^{\frac{1}{2}}}{2 z w x ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{\partial}{\partial x} ((\frac{y x}{z w})^{\frac{1}{2}})

Behandle

y, z, w

als Konstanten

Wende die Kettenregel an:

\frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (\frac{y x}{z w})

= \frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (\frac{y x}{z w})

\frac{\partial}{\partial x} (\frac{y x}{z w}) = \frac{y}{z w}

= \frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \cdot \frac{y}{z w}

Vereinfache

\frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \cdot \frac{y}{z w} : \frac{y ^{\frac{1}{2}} ( z w ) ^{\frac{1}{2}}}{2 z w x ^{\frac{1}{2}}}

= \frac{y ^{\frac{1}{2}} ( z w ) ^{\frac{1}{2}}}{2 z w x ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{4 - x e ^{x}}{x + e ^{x}})

n = 1 \sum \infty \frac{cos ( nπ )}{n ^{2}}

x \to 2 lim (\frac{x + 47 - 7}{5 x - 10})

\frac{\partial}{\partial x} (y^{5} sin (6 x))

\int_{0}^{1} \int_{0}^{s^{5}} cos (s^{6}) d t d s