derivative of 1/(1+2x)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (9 + 5 x)

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

n = 1 \sum \infty n! 2^{n} n^{- n}

d er i v a t i v e 1 + 4 x^{2}

l a pl a ce t r an s f or m 5 (t - 4)