derivative of 1/(3+(2x+1^2))

Lösung

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

- \frac{2 x + 1}{4 ( x ^{2} + x + 1 ) ^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (3 + (2 x + 1)^{2}) = 8 x + 4

= - \frac{1}{( 3 + ( 2 x + 1 ) ^{2} ) ^{2}} (8 x + 4)

Vereinfache

- \frac{1}{( 3 + ( 2 x + 1 ) ^{2} ) ^{2}} (8 x + 4) : - \frac{2 x + 1}{4 ( x ^{2} + x + 1 ) ^{2}}

= - \frac{2 x + 1}{4 ( x ^{2} + x + 1 ) ^{2}}

cos (t) y^{^{'}} + sin (t) y - 1 = 0

t an g e n t f (x) = 2 x, (1, 2)

\int \frac{4}{x ( x - 4 ) ^{2}} d x

x \to 1 + lim (arcsin (x))

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