derivative of sqrt((3x^{-2)+2/(x^2+8)})

Lösung

\frac{d}{d x} (\frac{3 x ^{- 2} + 2}{x ^{2} + 8})

- \frac{2 ( x ^{4} + 3 x ^{2} + 12 )}{x ^{2} 2 x ^{2} + 3 ( x ^{2} + 8 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{- 2} + 2}{x ^{2} + 8})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{3 x ^{- 2} + 2}{x ^{2} + 8}) = \frac{- 4 x ^{4} - 12 x ^{2} - 48}{x ^{3} ( x ^{2} + 8 ) ^{2}}

= \frac{1}{2 \frac{3 x ^{- 2} + 2}{x ^{2} + 8}} \cdot \frac{- 4 x ^{4} - 12 x ^{2} - 48}{x ^{3} ( x ^{2} + 8 ) ^{2}}

Vereinfache

\frac{1}{2 \frac{3 x ^{- 2} + 2}{x ^{2} + 8}} \cdot \frac{- 4 x ^{4} - 12 x ^{2} - 48}{x ^{3} ( x ^{2} + 8 ) ^{2}} : - \frac{2 ( x ^{4} + 3 x ^{2} + 12 )}{x ^{2} 2 x ^{2} + 3 ( x ^{2} + 8 ) ^{\frac{3}{2}}}

= - \frac{2 ( x ^{4} + 3 x ^{2} + 12 )}{x ^{2} 2 x ^{2} + 3 ( x ^{2} + 8 ) ^{\frac{3}{2}}}

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

in v erse l a pl a ce \frac{( 12 s + 3 )}{s ^{2} ( 2 s + 8 )}

\int \frac{1}{- x ^{- 2} + 2 x} d x

y^{^{'}} + \frac{y}{9.33} = 6.429

y^{^{''}} = x^{4}