derivative of 1/(x^2+9)

Lösung

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

s l o p e (3, - 6), (5, - 5)

a re a y = x^{3} - 1, y = x - 1

x \to 1 lim (x + 3 e x - 1 + 1)

d er i v a t i v e 1. 8^{2 x}

in v erse l a pl a ce \frac{( 2 s + 1 )}{s ^{2} + 2 s + 1}