derivative of 1/(x^2+16)

Lösung

\frac{d}{d x} (\frac{1}{x ^{2} + 16})

- \frac{2 x}{( x ^{2} + 16 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{2} + 16})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{2} + 16)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x ^{2} + 16 ) ^{2}} \frac{d}{d x} (x^{2} + 16)

= - \frac{1}{( x ^{2} + 16 ) ^{2}} \frac{d}{d x} (x^{2} + 16)

\frac{d}{d x} (x^{2} + 16) = 2 x

= - \frac{1}{( x ^{2} + 16 ) ^{2}} \cdot 2 x

Vereinfache

- \frac{1}{( x ^{2} + 16 ) ^{2}} \cdot 2 x : - \frac{2 x}{( x ^{2} + 16 ) ^{2}}

= - \frac{2 x}{( x ^{2} + 16 ) ^{2}}

\int_{0}^{4} 4 x + 9 d x

\int_{- 9}^{9} 81 - x^{2} d x

l a pl a ce t r an s f or m 4 t^{2} - 3 cos (2 t) + 5 e^{- t}

a re a x - 1, x - 1

\frac{d}{d x} (∣ x ∣)