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Beliebt Rechnen >

derivative of sqrt(x*y)

Lösung

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

Lösung

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

Schritte zur Lösung

\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

integral of 2xy^3

\int 2 x y^{3} d x

integral of x^2cos(3x)

\int x^{2} cos (3 x) d x

integral of (r^3)/(sqrt(16+r^2))

\int \frac{r ^{3}}{16 + r ^{2}} d r

integral from 0 to 6 of |x-4|

\int_{0}^{6} ∣ x - 4 ∣ d x

derivative of ln((x+6^{11}))

\frac{d}{d x} (ln ((x + 6)^{11}))