derivative g(x)= 1/(4x^2+2x)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

l a pl a ce t r an s f or m 2 t + 3 t \cdot cos (2 t)

\frac{d}{d x} (c x e^{- x})

\int 2 x \cdot sin (x) e^{x} d x

t \cdot t y^{^{''}} + 5 t y^{^{'}} + 4 y = 0

(\frac{x ^{2} + 25}{2} + \frac{9 - x}{3})^{^{'}}