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Beliebt Rechnen >

derivative of (3x-9/(2x+8))

Lösung

\frac{d}{d x} (\frac{3 x - 9}{2 x + 8})

Lösung

\frac{21}{2 ( x + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - 9}{2 x + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x - 9 ) ( 2 x + 8 ) - \frac{d}{d x} ( 2 x + 8 ) ( 3 x - 9 )}{( 2 x + 8 ) ^{2}}

\frac{d}{d x} (3 x - 9) = 3

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

= \frac{3 ( 2 x + 8 ) - 2 ( 3 x - 9 )}{( 2 x + 8 ) ^{2}}

Vereinfache

\frac{3 ( 2 x + 8 ) - 2 ( 3 x - 9 )}{( 2 x + 8 ) ^{2}} : \frac{21}{2 ( x + 4 ) ^{2}}

= \frac{21}{2 ( x + 4 ) ^{2}}

Graph

Beliebte Beispiele

integral from 0 to pi/6 of sec^2(x)

\int_{0}^{\frac{π}{6}} sec^{2} (x) d x

tangent f(x)=x^3+2x

t an g e n t f (x) = x^{3} + 2 x

(\partial)/(\partial x)(xe^{xy}+x/(y^2))

\frac{\partial}{\partial x} (x e^{x y} + \frac{x}{y ^{2}})

tangent f(x)=sqrt(x),\at x=64

t an g e n t f (x) = x, at x = 64

4xyy^'=4y^2+3xsqrt(x^2+y^2)

4 x y y^{^{'}} = 4 y^{2} + 3 x x^{2} + y^{2}