derivative 7/(x^2+3)

Lösung

ableitung von

\frac{7}{x ^{2} + 3}

- \frac{14 x}{( x ^{2} + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7}{x ^{2} + 3})

Entferne die Konstante:

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

= 7 \frac{d}{d x} (\frac{1}{x ^{2} + 3})

Wende Exponentenregel an:

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

= 7 \frac{d}{d x} ((x^{2} + 3)^{- 1})

Wende die Kettenregel an:

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

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

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

= 7 (- \frac{1}{( x ^{2} + 3 ) ^{2}} \cdot 2 x)

Vereinfache

7 (- \frac{1}{( x ^{2} + 3 ) ^{2}} \cdot 2 x) : - \frac{14 x}{( x ^{2} + 3 ) ^{2}}

= - \frac{14 x}{( x ^{2} + 3 ) ^{2}}

\int_{- 1}^{1} e^{y} - y^{2} - 6 d y

\int sin^{5} (t) d t

\int (x^{20} - 5 x^{4})^{6} (x^{19} - x^{3}) d x

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

t an g e n t f (x) = x^{2} + 5 x - 3, at x = - 3