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Beliebt Rechnen >

derivative of (3x^2+2sqrt(x)/x)

Lösung

\frac{d}{d x} (\frac{3 x ^{2} + 2 x}{x})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2} + 2 x}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 3 x ^{2} + 2 x ) x - \frac{d x}{d x} ( 3 x ^{2} + 2 x )}{x ^{2}}

\frac{d}{d x} (3 x^{2} + 2 x) = 6 x + \frac{1}{x}

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

= \frac{( 6 x + \frac{1}{x} ) x - 1 \cdot ( 3 x ^{2} + 2 x )}{x ^{2}}

Vereinfache

\frac{( 6 x + \frac{1}{x} ) x - 1 \cdot ( 3 x ^{2} + 2 x )}{x ^{2}} : \frac{3 x ^{2} - x}{x ^{2}}

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

Graph

Beliebte Beispiele

derivative of cot(xcsc(x))

\frac{d}{d x} (cot (x) csc (x))

derivative g(x)=e^{x^2-x}

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

derivative of-2x+6

\frac{d}{d x} (- 2 x + 6)

integral of 8/(xln(5x))

\int \frac{8}{x ln ( 5 x )} d x

sum from n=1 to infinity of 1/(3n-1)

n = 1 \sum \infty \frac{1}{3 n - 1}