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Beliebt Rechnen >

derivative of sqrt(x)(x+1)

Lösung

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

Lösung

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of ln(2xy+4)

\frac{d}{d x} (ln (2 x y + 4))

integral of sec(t)(8sec(t)+7tan(t))

\int sec (t) (8 sec (t) + 7 tan (t)) d t

derivative of (-8x-2/(9x-4))

\frac{d}{d x} (\frac{- 8 x - 2}{9 x - 4})

inverselaplace e^{ax}

in v erse l a pl a ce e^{a x}

f^{^{'}} (x) = x - 1