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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{5 x ^{2} + 1}{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= \frac{5 x ^{2} + 1}{2 x}

Graph

Beliebte Beispiele

derivative of (3x^4-18x^5*cos(5x^2))

\frac{d}{d x} ((3 x^{4} - 18 x)^{5} \cdot cos (5 x^{2}))

(yx-y)dy-(y+1)dx=0

(y x - y) d y - (y + 1) d x = 0

integral of e^{-x}*sin(2x)

\int e^{- x} \cdot sin (2 x) d x

integral of (arctan(x)-ln(x))

\int (arctan (x) - ln (x)) d x

integral of (12x+7)

\int (12 x + 7) d x