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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{3}{4 ( 3 x - 1 ) ^{\frac{3}{2}}}

t an g e n t f (x) = 8 (x - \frac{1}{x})^{4}, at x = 2

d e g 2 r a d (sin (x^{'}))^{^{'}}

d er i v a t i v e x - 2 + \frac{( x + 1 ) ^{2}}{2}

\int_{0}^{1} π (y - y^{2}) d y

d er i v a t i v e 3 t^{2} + 4 t^{5}