derivative of (2x-x^2/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{2 x - x ^{2}}{x})

\frac{2 - 3 x}{2 x}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x - x ^{2}}{x})

Vereinfache

\frac{2 x - x ^{2}}{x} : x (2 - x)

= \frac{d}{d x} (x (2 - x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 2 - x

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

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

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

= \frac{1}{2 x} (2 - x) + (- 1) x

Vereinfache

\frac{1}{2 x} (2 - x) + (- 1) x : \frac{2 - 3 x}{2 x}

= \frac{2 - 3 x}{2 x}

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 40 cos (8 t)

(6 x + 1) y^{2} \frac{d y}{d x} + 3 x^{2} + 2 y^{3} = 0

x \to 3 + lim (\frac{3 x + 4}{x - 3})

(e^{x} - 1)^{^{'}}

\frac{d}{d x} (arcsin (sin (7 x)))