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Beliebt Rechnen >

derivative of 6/(2x+1)

Lösung

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

Lösung

- \frac{12}{( 2 x + 1 ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

6 (- \frac{1}{( 2 x + 1 ) ^{2}} \cdot 2) : - \frac{12}{( 2 x + 1 ) ^{2}}

= - \frac{12}{( 2 x + 1 ) ^{2}}

Graph

Beliebte Beispiele

derivative of sqrt(((x+1/(x+6))^8))

\frac{d}{d x} (\frac{x + 1}{x + 6})^{8}

y^'= 1/((t-1)(y+1))

y^{^{'}} = \frac{1}{( t - 1 ) ( y + 1 )}

derivative f(x)=x^3(x-6)^2

d er i v a t i v e f (x) = x^{3} (x - 6)^{2}

f(x)=sqrt(x-1)+sqrt(x+1)

f (x) = x - 1 + x + 1

tangent y=(((x+2))/((x-2)))^2,\at x=3

t an g e n t y = (\frac{( x + 2 )}{( x - 2 )})^{2}, at x = 3