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

Lösung

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

- \frac{6}{( 2 x + 1 ) ^{\frac{3}{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)^{- \frac{1}{2}})

Wende die Kettenregel an:

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

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

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

= 6 (- \frac{1}{2 ( 2 x + 1 ) ^{\frac{3}{2}}} \cdot 2)

Vereinfache

6 (- \frac{1}{2 ( 2 x + 1 ) ^{\frac{3}{2}}} \cdot 2) : - \frac{6}{( 2 x + 1 ) ^{\frac{3}{2}}}

= - \frac{6}{( 2 x + 1 ) ^{\frac{3}{2}}}

d er i v a t i v e tan^{3} (x)

\frac{d}{d x} (\frac{150}{x})

\frac{d y}{d x} = 4 x

l a pl a ce t r an s f or m e^{1}

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