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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

derivative of 1/2 ln^2(x)

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

derivative-7csc(5x)e^{3x}

d er i v a t i v e - 7 csc (5 x) e^{3 x}

integral from-2 to 2x of (3t^2+2t)

\int_{- 2}^{2 x} (3 t^{2} + 2 t) d t

inverselaplace 3/(2s+1)

in v erse l a pl a ce \frac{3}{2 s + 1}

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d er i v a t i v e f (x) = 2 x + 1