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

Lösung

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

\frac{44}{x ^{2}} + \frac{27}{x ^{4}} + 5

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = \frac{1}{x ^{2}} - \frac{9}{x ^{4}}, g = x + 5 x^{3}

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

\frac{d}{d x} (\frac{1}{x ^{2}} - \frac{9}{x ^{4}}) = - \frac{2}{x ^{3}} + \frac{36}{x ^{5}}

\frac{d}{d x} (x + 5 x^{3}) = 1 + 15 x^{2}

= (- \frac{2}{x ^{3}} + \frac{36}{x ^{5}}) (x + 5 x^{3}) + (1 + 15 x^{2}) (\frac{1}{x ^{2}} - \frac{9}{x ^{4}})

Vereinfache

(- \frac{2}{x ^{3}} + \frac{36}{x ^{5}}) (x + 5 x^{3}) + (1 + 15 x^{2}) (\frac{1}{x ^{2}} - \frac{9}{x ^{4}}) : \frac{44}{x ^{2}} + \frac{27}{x ^{4}} + 5

= \frac{44}{x ^{2}} + \frac{27}{x ^{4}} + 5

x \to 0 lim (2 e^{3 x})

t an g e n t f (x) = \frac{12 x}{x ^{2} - 4}, (4, 4)

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

d er i v a t i v e \frac{8 x ^{2} + 9}{x ^{2} + 5}

l a pl a ce t r an s f or m 45