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Beliebt Rechnen >

derivative of 2sqrt(xy)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \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}

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

Vereinfache

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

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

Beliebte Beispiele

x^{^{'}} = 6 (x^{2} + 1)

derivative of 10^{x^2}

\frac{d}{d x} (1 0^{x^{2}})

integral from 0 to 4 of 1/(sqrt(9+x^2))

\int_{0}^{4} \frac{1}{9 + x ^{2}} d x

(\partial)/(\partial x)(-6x+12)

\frac{\partial}{\partial x} (- 6 x + 12)

fläche y^2=4x,y=4x-2

a re a y^{2} = 4 x, y = 4 x - 2