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Beliebt Rechnen >

derivative (2x^2+1)/(x^2+8)

Lösung

ableitung von

\frac{2 x ^{2} + 1}{x ^{2} + 8}

Lösung

\frac{30 x}{( x ^{2} + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{2} + 1}{x ^{2} + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} + 1 ) ( x ^{2} + 8 ) - \frac{d}{d x} ( x ^{2} + 8 ) ( 2 x ^{2} + 1 )}{( x ^{2} + 8 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 8) = 2 x

= \frac{4 x ( x ^{2} + 8 ) - 2 x ( 2 x ^{2} + 1 )}{( x ^{2} + 8 ) ^{2}}

Multipliziere aus

4 x (x^{2} + 8) - 2 x (2 x^{2} + 1) : 30 x

= \frac{30 x}{( x ^{2} + 8 ) ^{2}}

Graph

Beliebte Beispiele

integral from 0 to 1 of ln(x^2+1)

\int_{0}^{1} ln (x^{2} + 1) d x

integral of 1/(x^2+x+1)

\int \frac{1}{x ^{2} + x + 1} d x

derivative-(3(z^2+1))/(z^2)

d er i v a t i v e - \frac{3 ( z ^{2} + 1 )}{z ^{2}}

fläche y^2=6-x,3y=x+12

a re a y^{2} = 6 - x, 3 y = x + 12

integral from pi to 2pi of 9xsin(x)

\int_{π}^{2 π} 9 x sin (x) d x