derivative of 1/(sqrt(4-x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 1 lim ((1 - x^{2})^{1 - x})

\frac{d}{d v} (u + v)

\int (1 + x)^{2} d x

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

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