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Beliebt Rechnen >

derivative of (3x-1/(x+1))

Lösung

\frac{d}{d x} (\frac{3 x - 1}{x + 1})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - 1}{x + 1})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (3 x - 1) = 3

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

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

Vereinfache

\frac{3 ( x + 1 ) - 1 \cdot ( 3 x - 1 )}{( x + 1 ) ^{2}} : \frac{4}{( x + 1 ) ^{2}}

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

Graph

Beliebte Beispiele

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

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

derivative of 8(0.9^{x-2})

\frac{d}{d x} (8 (0.9)^{x - 2})

xy^'=y^2-y,y(2)=1

x y^{^{'}} = y^{2} - y, y (2) = 1

integral from 0 to 1 of 1/((x^2+1)^3)

\int_{0}^{1} \frac{1}{( x ^{2} + 1 ) ^{3}} d x

tangent f(x)=3x^2-5x+8,\at x=2

t an g e n t f (x) = 3 x^{2} - 5 x + 8, at x = 2