derivative of 3/(x^2+1)

Lösung

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

- \frac{6 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

3 (- \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 2 x) : - \frac{6 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{6 x}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (\frac{1}{x ^{6}} + \frac{1}{x ^{7}})

d er i v a t i v e (x^{2} + 8) (5 - x)

t an g e n t f (x) = \frac{- 8 x}{x ^{2} + 1}, (- 1, 4)

\int \frac{tan ( x )}{csc ( x ) + cot ( x )} d x

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