(\partial)/(\partial y)(4x^{y/z})

Lösung

\frac{\partial}{\partial y} (4 x^{\frac{y}{z}})

\frac{4 x ^{\frac{y}{z}} ln ( x )}{z}

Schritte zur Lösung

\frac{\partial}{\partial y} (4 x^{\frac{y}{z}})

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

= 4 \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)}

= 4 \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}

= 4 e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z}

Vereinfache

4 e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z} : \frac{4 x ^{\frac{y}{z}} ln ( x )}{z}

= \frac{4 x ^{\frac{y}{z}} ln ( x )}{z}

\int_{0}^{4} x^{3} 7 - x^{2} d x

t an g e n t f (x) = x^{3} - \frac{2}{x ^{2}} + 2, (1, 3)

\frac{\partial}{\partial x} (x^{1})

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

\int_{0}^{\frac{3 π}{2}} cos^{3} (29 x) d x