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Beliebt Rechnen >

derivative of x^2sqrt(x-4)

Lösung

\frac{d}{d x} (x^{2} x - 4)

Lösung

\frac{5 x ^{2} - 16 x}{2 x - 4}

Schritte zur Lösung

\frac{d}{d x} (x^{2} x - 4)

Wende die Produktregel an:

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

f = x^{2}, g = x - 4

= \frac{d}{d x} (x^{2}) x - 4 + \frac{d}{d x} (x - 4) x^{2}

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

\frac{d}{d x} (x - 4) = \frac{1}{2 x - 4}

= 2 x x - 4 + \frac{1}{2 x - 4} x^{2}

Vereinfache

2 x x - 4 + \frac{1}{2 x - 4} x^{2} : \frac{5 x ^{2} - 16 x}{2 x - 4}

= \frac{5 x ^{2} - 16 x}{2 x - 4}

Graph

Beliebte Beispiele

t a y l or cos (x)

limit as x approaches 0 of x^2-sin(1/x)

x \to 0 lim (x^{2} - sin (\frac{1}{x}))

derivative y=x^3(2x+3)^7

d er i v a t i v e y = x^{3} (2 x + 3)^{7}

fläche 3x, 3/x ,x=3

a re a 3 x, \frac{3}{x}, x = 3

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