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Beliebt Rechnen >

(\partial)/(\partial z)(2x^{y/z})

Lösung

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

Lösung

- \frac{2 y x ^{\frac{y}{z}} ln ( x )}{z ^{2}}

Schritte zur Lösung

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

Behandle

x, y

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{\frac{y}{z}} = e^{\frac{y}{z} l n (x)}

= 2 \frac{\partial}{\partial z} (e^{\frac{y}{z} l n (x)})

Wende die Kettenregel an:

e^{\frac{y}{z} l n (x)} \frac{\partial}{\partial z} (\frac{y}{z} ln (x))

= e^{\frac{y}{z} l n (x)} \frac{\partial}{\partial z} (\frac{y}{z} ln (x))

\frac{\partial}{\partial z} (\frac{y}{z} ln (x)) = - \frac{y ln ( x )}{z ^{2}}

= 2 e^{\frac{y}{z} l n (x)} (- \frac{y ln ( x )}{z ^{2}})

Vereinfache

2 e^{\frac{y}{z} l n (x)} (- \frac{y ln ( x )}{z ^{2}}) : - \frac{2 y x ^{\frac{y}{z}} ln ( x )}{z ^{2}}

= - \frac{2 y x ^{\frac{y}{z}} ln ( x )}{z ^{2}}

Beliebte Beispiele

tangent y=4sqrt(x)

t an g e n t y = 4 x

(\partial)/(\partial x)(x^3y^2-4yx^2+3yx-4)

\frac{\partial}{\partial x} (x^{3} y^{2} - 4 y x^{2} + 3 y x - 4)

tangent y=x^2+5x+6,\at x=7

t an g e n t y = x^{2} + 5 x + 6, at x = 7

integral of sqrt(144-9x^2)

\int 144 - 9 x^{2} d x

limit as x approaches-5+of 3/(x^2-25)

x \to - 5 + lim (\frac{3}{x ^{2} - 25})