derivative f(x)=xsqrt(x-x^2)

Lösung

ableitung von

f (x) = x x - x^{2}

\frac{- 4 x ^{2} + 3 x}{2 x - x ^{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = x - x^{2}

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

\frac{d x}{d x} = 1

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

= 1 \cdot x - x^{2} + \frac{1 - 2 x}{2 x - x ^{2}} x

Vereinfache

1 \cdot x - x^{2} + \frac{1 - 2 x}{2 x - x ^{2}} x : \frac{- 4 x ^{2} + 3 x}{2 x - x ^{2}}

= \frac{- 4 x ^{2} + 3 x}{2 x - x ^{2}}

t an g e n t e^{x}, ln (12)

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

x \to 0 lim (\frac{9}{x})

\frac{d y}{d x} = - \frac{1 + x + y}{1 + x}

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0