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Beliebt Rechnen >

(\partial)/(\partial y)(9x^{y/z})

Lösung

\frac{\partial}{\partial y} (9 x^{\frac{y}{z}})

Lösung

\frac{9 x ^{\frac{y}{z}} ln ( x )}{z}

Schritte zur Lösung

\frac{\partial}{\partial y} (9 x^{\frac{y}{z}})

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

= 9 \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)}

= 9 \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}

= 9 e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z}

Vereinfache

9 e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z} : \frac{9 x ^{\frac{y}{z}} ln ( x )}{z}

= \frac{9 x ^{\frac{y}{z}} ln ( x )}{z}

Beliebte Beispiele

derivative of (sin(3x)/(cos(2x)))

\frac{d}{d x} (\frac{sin ( 3 x )}{cos ( 2 x )})

derivative arcsin(x/9)

d er i v a t i v e arcsin (\frac{x}{9})

tangent f(x)=(e^x)/x ,e,\at x=1

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

integral of (9x-6)^2

\int (9 x - 6)^{2} d x

derivative-xe^x

d er i v a t i v e - x e^{x}