(\partial)/(\partial x)((x/y)^z)

Lösung

\frac{\partial}{\partial x} ((\frac{x}{y})^{z})

\frac{z x ^{z - 1}}{y ^{z}}

Schritte zur Lösung

\frac{\partial}{\partial x} ((\frac{x}{y})^{z})

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

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

Vereinfache

z (\frac{x}{y})^{z - 1} \frac{1}{y} : \frac{z x ^{z - 1}}{y ^{z}}

= \frac{z x ^{z - 1}}{y ^{z}}

\int_{1}^{2} \frac{9 ln ( x )}{x ^{2}} d x

t an g e n t f (x) = x^{2} - \frac{1}{x}, at x = 2

\frac{d}{d y} (e^{\frac{y}{x}})

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

\int (e^{3 x} - 1)^{3} d x