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Beliebt Rechnen >

(\partial)/(\partial y)(x^{1/4}y^{3/4})

Lösung

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

Lösung

\frac{3 x ^{\frac{1}{4}}}{4 y ^{\frac{1}{4}}}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

= \frac{3 x ^{\frac{1}{4}}}{4 y ^{\frac{1}{4}}}

Beliebte Beispiele

integral from-infinity to 0 of 1/(4-8x)

\int_{- \infty}^{0} \frac{1}{4 - 8 x} d x

y^'= x/((1+2y)),y(-1)=0

y^{^{'}} = \frac{x}{( 1 + 2 y )}, y (- 1) = 0

derivative of cos(x-2sin(x))

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

limit as x approaches 5-of 2/(x-5)

x \to 5 - lim (\frac{2}{x - 5})

derivative of x^2y^3+xe^{xy}

\frac{d}{d x} (x^{2} y^{3} + x e^{x y})