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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{3 y}{( 2 + 3 y ^{2} ) ^{3}} d y

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

\int 1 + sin (x) d x

d er i v a t i v e f (x) = 5 + 4 e^{3 x}

y^{^{''}} + 16 y^{^{'}} + 64 y = 0, y (0) = - 3, y^{^{'}} (0) = 28