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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

2 x (2 x + 3) - 2 x^{2} : 2 x^{2} + 6 x

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

Graph

Beliebte Beispiele

y^{^{'}} + 4 x y = 0

integral of 4(2x+5)^3

\int 4 (2 x + 5)^{3} d x

taylor sqrt(1-x^2),x=0

t a y l or 1 - x^{2}, x = 0

derivative of (x^2/(3+8x))

\frac{d}{d x} (\frac{x ^{2}}{3 + 8 x})

x \cdot y^{^{'}} + y^{2} = 0