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Beliebt Rechnen >

derivative of (2x+1/(x-3))

Lösung

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

Lösung

- \frac{7}{( x - 3 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 ( x - 3 ) - 1 \cdot ( 2 x + 1 )}{( x - 3 ) ^{2}} : - \frac{7}{( x - 3 ) ^{2}}

= - \frac{7}{( x - 3 ) ^{2}}

Graph

Beliebte Beispiele

derivative of sin(ln(3x^2+x))

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

derivative of-(10/(10-x))

\frac{d}{d x} (- \frac{10}{10 - x})

integral of 1/(x*sqrt(1-x^2))

\int \frac{1}{x \cdot 1 - x ^{2}} d x

derivative of axe^{2x}

\frac{d}{d x} (a x e^{2 x})

tangent f(x)=x^3+x^2+(6/x),\at x=1

t an g e n t f (x) = x^{3} + x^{2} + (\frac{6}{x}), at x = 1