derivative of (1/(x^2-5/(x^4))(x+9x^3))

Lösung

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 9 x^{3}))

\frac{44}{x ^{2}} + \frac{15}{x ^{4}} + 9

Schritte zur Lösung

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 9 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 + 9 x^{3}

= \frac{d}{d x} (\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 9 x^{3}) + \frac{d}{d x} (x + 9 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 + 9 x^{3}) = 1 + 27 x^{2}

= (- \frac{2}{x ^{3}} + \frac{20}{x ^{5}}) (x + 9 x^{3}) + (1 + 27 x^{2}) (\frac{1}{x ^{2}} - \frac{5}{x ^{4}})

Vereinfache

(- \frac{2}{x ^{3}} + \frac{20}{x ^{5}}) (x + 9 x^{3}) + (1 + 27 x^{2}) (\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) : \frac{44}{x ^{2}} + \frac{15}{x ^{4}} + 9

= \frac{44}{x ^{2}} + \frac{15}{x ^{4}} + 9

x \to 0 + lim (\frac{( 3 )}{x ^{2} - x})

\int_{0}^{8} \frac{x}{( x + 8 ) ^{3}} d x

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

\int \frac{x}{x - 1} d x

d er i v a t i v e y = \frac{e ^{x}}{5 x ^{2}}