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Beliebt Rechnen >

derivative of (x-3sqrt(x))

Lösung

\frac{d}{d x} ((x - 3) x)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} ((x - 3) x)

Wende die Produktregel an:

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

f = x - 3, g = x

= \frac{d}{d x} (x - 3) x + \frac{d}{d x} (x) (x - 3)

\frac{d}{d x} (x - 3) = 1

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (ln(z))/(z^2)

\int \frac{ln ( z )}{z ^{2}} d z

integral from-1 to 3 of (4x^2-7)/(2x+3)

\int_{- 1}^{3} \frac{4 x ^{2} - 7}{2 x + 3} d x

derivative of In

\frac{d}{d x} (I n)

(dy)/(dx)=12x^3y

\frac{d y}{d x} = 12 x^{3} y

integral of (e^x+1)(e^x+x)

\int (e^{x} + 1) (e^{x} + x) d x