derivative (x^4+3x)^{-1}

Lösung

ableitung von

(x^{4} + 3 x)^{- 1}

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (x^{2} + \frac{3456}{x})

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 81 )}

\frac{d}{d x} (\frac{d y}{d x}) + 81 y = 0

\int cos (\frac{u}{v}) d u

x \to + 0 lim (\frac{sin ( 0 )}{0})