derivative 1/(1+5x^2)

Lösung

ableitung von

\frac{1}{1 + 5 x ^{2}}

- \frac{10 x}{( 1 + 5 x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{1 + 5 x ^{2}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((1 + 5 x^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 1 + 5 x ^{2} ) ^{2}} \frac{d}{d x} (1 + 5 x^{2})

= - \frac{1}{( 1 + 5 x ^{2} ) ^{2}} \frac{d}{d x} (1 + 5 x^{2})

\frac{d}{d x} (1 + 5 x^{2}) = 10 x

= - \frac{1}{( 1 + 5 x ^{2} ) ^{2}} \cdot 10 x

Vereinfache

- \frac{1}{( 1 + 5 x ^{2} ) ^{2}} \cdot 10 x : - \frac{10 x}{( 1 + 5 x ^{2} ) ^{2}}

= - \frac{10 x}{( 1 + 5 x ^{2} ) ^{2}}

t an g e n t f (x) = 5 x + 1, at x = 7

\int cos (ln (x)) d x

\int \frac{x ^{2}}{49 + x ^{2}} d x

y^{^{'}} + y = 2, y (0) = 0

s l o p e (- 5.3) (7.9)