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Beliebt Rechnen >

derivative f(x)= 1/(sqrt(2x+3))

Lösung

ableitung von

f (x) = \frac{1}{2 x + 3}

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (x^3+2x)^5(6x^2+4)

\int (x^{3} + 2 x)^{5} (6 x^{2} + 4) d x

derivative of ln(x/(2e))

\frac{d}{d x} (ln (\frac{x}{2 e}))

tangent f(x)=x^2+9,(-2,13)

t an g e n t f (x) = x^{2} + 9, (- 2, 13)

integral from 0 to 2 of 1/(x-1)

\int_{0}^{2} \frac{1}{x - 1} d x

integral of (x/(sqrt(x+1)))

\int (\frac{x}{x + 1}) d x