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Beliebt Rechnen >

(\partial)/(\partial y)(7x^{y/z})

Lösung

\frac{\partial}{\partial y} (7 x^{\frac{y}{z}})

Lösung

\frac{7 x ^{\frac{y}{z}} ln ( x )}{z}

Schritte zur Lösung

\frac{\partial}{\partial y} (7 x^{\frac{y}{z}})

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

= 7 \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)}

= 7 \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}

= 7 e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z}

Vereinfache

7 e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z} : \frac{7 x ^{\frac{y}{z}} ln ( x )}{z}

= \frac{7 x ^{\frac{y}{z}} ln ( x )}{z}

Beliebte Beispiele

y^'+(2y)/x = 2/x

y^{^{'}} + \frac{2 y}{x} = \frac{2}{x}

integral of u/(u+1)

\int \frac{u}{u + 1} d u

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x \to 2 lim (sin (\frac{1}{x} - \frac{1}{2}))

integral of xsqrt(4x+1)

\int x 4 x + 1 d x

f(x)=sqrt(5)x+sqrt(7x)

f (x) = 5 x + 7 x