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Beliebt Rechnen >

(\partial)/(\partial y)((x-5)^{1/4}y^{1/4})

Lösung

\frac{\partial}{\partial y} ((x - 5)^{\frac{1}{4}} y^{\frac{1}{4}})

Lösung

\frac{( x - 5 ) ^{\frac{1}{4}}}{4 y ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{\partial}{\partial y} ((x - 5)^{\frac{1}{4}} y^{\frac{1}{4}})

Behandle

x

als Konstante

Entferne die Konstante:

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

= (x - 5)^{\frac{1}{4}} \frac{\partial}{\partial y} (y^{\frac{1}{4}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= (x - 5)^{\frac{1}{4}} \frac{1}{4} y^{\frac{1}{4} - 1}

Vereinfache

(x - 5)^{\frac{1}{4}} \frac{1}{4} y^{\frac{1}{4} - 1} : \frac{( x - 5 ) ^{\frac{1}{4}}}{4 y ^{\frac{3}{4}}}

= \frac{( x - 5 ) ^{\frac{1}{4}}}{4 y ^{\frac{3}{4}}}

Beliebte Beispiele

derivative of x^{sqrt(x)+1}

\frac{d}{d x} (x^{x + 1})

derivative of-e^{-xy}

\frac{d}{d x} (- e^{- x y})

integral from 1 to infinity of (e^{-x})

\int_{1}^{\infty} (e^{- x}) d x

integral of 6/(x-1)

\int \frac{6}{x - 1} d x

integral of \sqrt[3]{(8-x)^4}

\int 3 (8 - x)^{4} d x