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Beliebt Rechnen >

derivative of (xy/(sqrt(xy)))

Lösung

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

Lösung

\frac{y + x \frac{d y}{d x}}{2 x y}

Schritte zur Lösung

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

Vereinfache

\frac{x y}{x y} : x y

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

Wende die Kettenregel an:

\frac{1}{2 x y} \frac{d}{d x} (x y)

= \frac{1}{2 x y} \frac{d}{d x} (x y)

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

= \frac{1}{2 x y} (y + x \frac{d y}{d x})

Vereinfache

\frac{1}{2 x y} (y + x \frac{d y}{d x}) : \frac{y + x \frac{d y}{d x}}{2 x y}

= \frac{y + x \frac{d y}{d x}}{2 x y}

Beliebte Beispiele

derivative of 6sin^2(x)

\frac{d}{d x} (6 sin^{2} (x))

\frac{d}{d t} (π t^{2})

integral of sqrt(16-r^2)r

\int 16 - r^{2} r d r

derivative 7/(\sqrt[4]{x)}

d er i v a t i v e \frac{7}{4 x}

y^{''}+7y^'+12=0

y^{^{''}} + 7 y^{^{'}} + 12 = 0