derivative of sqrt(2xy)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 2 x y} \cdot 2 (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}

d er i v a t i v e 10 x - 3 x^{2}

t an g e n t f (x) = 3 x^{2} - 5 x + 2, at x = - 1

\int_{0}^{2 π} e^{i (θ - x)} d x

\int \frac{4 x ^{2}}{4 x - x ^{2}} d x

\frac{d}{d x} (8 x e^{2 x})