derivative of \sqrt[4]{xy}

Lösung

\frac{d}{d x} (4 x y)

\frac{y + x \frac{d y}{d x}}{4 ( x y ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 x y)

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Vereinfache

\frac{1}{4 ( x y ) ^{\frac{3}{4}}} (y + x \frac{d y}{d x}) : \frac{y + x \frac{d y}{d x}}{4 ( x y ) ^{\frac{3}{4}}}

= \frac{y + x \frac{d y}{d x}}{4 ( x y ) ^{\frac{3}{4}}}

\frac{d}{d x} (x^{4 π})

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

\frac{d}{d v} (\frac{u}{v})

\int_{0}^{1} - 2 (x^{2} + 1) e^{- x} d x

d er i v a t i v e f (x) = arcsec (2 x)