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Beliebt Rechnen >

derivative of (6x+2/(x+1))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{6 ( x + 1 ) - 1 \cdot ( 6 x + 2 )}{( x + 1 ) ^{2}} : \frac{4}{( x + 1 ) ^{2}}

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

Graph

Beliebte Beispiele

derivative of (x+2sqrt(2x-3))

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

(\partial)/(\partial x)(x^2+3yz+4xy)

\frac{\partial}{\partial x} (x^{2} + 3 yz + 4 x y)

y^'=(xy^'+y)y^1985

y^{^{'}} = (x y^{^{'}} + y) y^{1} 985

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

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

(\partial)/(\partial y)(ln(2x^3+3y^2))

\frac{\partial}{\partial y} (ln (2 x^{3} + 3 y^{2}))