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Beliebt Rechnen >

derivative f(x)= 1/(sqrt(2x-1))

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

= \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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (28)/(28+e^x)

\int \frac{28}{28 + e ^{x}} d x

limit as x approaches 3+of 6+x

x \to 3 + lim (6 + x)

tangent y= 6/(x^2),(1,6)

t an g e n t y = \frac{6}{x ^{2}}, (1, 6)

integral of 1/(x^2(x^2-9))

\int \frac{1}{x ^{2} ( x ^{2} - 9 )} d x

tangent y=3x^3-x^2+5,(2,25)

t an g e n t y = 3 x^{3} - x^{2} + 5, (2, 25)