derivative of (x-1*sqrt(x^2-2x+2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x - 1, g = x^{2} - 2 x + 2

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

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

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

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

Vereinfache

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

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

\int \frac{2}{x ^{3} + x ^{2}} d x

\frac{d}{d y} (y^{\frac{2}{3}})

d er i v a t i v e y = (t^{2} + 8)^{2} - 2 (t^{2} + 8)

\frac{\partial}{\partial z} (e^{- x^{2} - 2 y^{2} - 3 z^{2}})

\int (3 x + 1)^{11} d x