derivative of 3/((4x^2-1^4))

Lösung

\frac{d}{d x} (\frac{3}{( 4 x ^{2} - 1 ) ^{4}})

- \frac{96 x}{( 4 x ^{2} - 1 ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{( 4 x ^{2} - 1 ) ^{4}})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{4}{( 4 x ^{2} - 1 ) ^{5}} \frac{d}{d x} (4 x^{2} - 1)

= - \frac{4}{( 4 x ^{2} - 1 ) ^{5}} \frac{d}{d x} (4 x^{2} - 1)

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

= 3 (- \frac{4}{( 4 x ^{2} - 1 ) ^{5}} \cdot 8 x)

Vereinfache

3 (- \frac{4}{( 4 x ^{2} - 1 ) ^{5}} \cdot 8 x) : - \frac{96 x}{( 4 x ^{2} - 1 ) ^{5}}

= - \frac{96 x}{( 4 x ^{2} - 1 ) ^{5}}

in v erse l a pl a ce \frac{20}{( s ^{2} + 4 ) ( s - 4 )}

x \to 2 lim (tan (\frac{π x}{4}))

\frac{\partial}{\partial x} (ln (\frac{2 x y}{7 z}))

t an g e n t f (x) = 1 3 x, at x = 1

\int (x + 2) sin (x) d x