derivative (1/(x^2)-5/(x^4))(x+8x^3)

Lösung

ableitung von

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

\frac{39}{x ^{2}} + \frac{15}{x ^{4}} + 8

Schritte zur Lösung

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 8 x^{3}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{x ^{2}} - \frac{5}{x ^{4}}, g = x + 8 x^{3}

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

\frac{d}{d x} (\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) = - \frac{2}{x ^{3}} + \frac{20}{x ^{5}}

\frac{d}{d x} (x + 8 x^{3}) = 1 + 24 x^{2}

= (- \frac{2}{x ^{3}} + \frac{20}{x ^{5}}) (x + 8 x^{3}) + (1 + 24 x^{2}) (\frac{1}{x ^{2}} - \frac{5}{x ^{4}})

Vereinfache

(- \frac{2}{x ^{3}} + \frac{20}{x ^{5}}) (x + 8 x^{3}) + (1 + 24 x^{2}) (\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) : \frac{39}{x ^{2}} + \frac{15}{x ^{4}} + 8

= \frac{39}{x ^{2}} + \frac{15}{x ^{4}} + 8

\int 7 x^{3} (x - 5)^{- 4} d x

in v erse l a pl a ce \frac{2}{s} + \frac{3}{s + 1}

\frac{d}{d x} (\frac{( 4 x ^{2} + 6 x + 4 )}{x})

t a y l or \frac{( e ^{t} )}{1 + t}

\frac{d}{d x} (\frac{24}{( x + 1 ) ^{5}})