derivative of 1/(sqrt(x^2+9))

Lösung

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

- \frac{x}{( x ^{2} + 9 ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{1}{2 ( x ^{2} + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} + 9)

= - \frac{1}{2 ( x ^{2} + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} + 9)

\frac{d}{d x} (x^{2} + 9) = 2 x

= - \frac{1}{2 ( x ^{2} + 9 ) ^{\frac{3}{2}}} \cdot 2 x

Vereinfache

- \frac{1}{2 ( x ^{2} + 9 ) ^{\frac{3}{2}}} \cdot 2 x : - \frac{x}{( x ^{2} + 9 ) ^{\frac{3}{2}}}

= - \frac{x}{( x ^{2} + 9 ) ^{\frac{3}{2}}}

\int \frac{5 x ^{2}}{x ^{2} + 7} d x

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

\frac{d}{d x} (\frac{3}{4} x^{2} - 5 x^{3})