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Beliebt Rechnen >

derivative of xsqrt(x-1)

Lösung

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

Lösung

\frac{3 x - 2}{2 x - 1}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = x - 1

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

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

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

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

Vereinfache

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

= \frac{3 x - 2}{2 x - 1}

Graph

Beliebte Beispiele

derivative y= x/((x-2)^2)

d er i v a t i v e y = \frac{x}{( x - 2 ) ^{2}}

derivative of (x^2+1*(x+5+1/x))

\frac{d}{d x} ((x^{2} + 1) \cdot (x + 5 + \frac{1}{x}))

(dy)/(dx)=e^{5x+4y}

\frac{d y}{d x} = e^{5 x + 4 y}

integral from 2 to infinity of 9/(2x^2)

\int_{2}^{\infty} \frac{9}{2 x ^{2}} d x

integral of 5xcos(x)

\int 5 x cos (x) d x