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

Lösung

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

\frac{26}{x ^{2}} + \frac{27}{x ^{4}} + 3

Schritte zur Lösung

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

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

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

Vereinfache

(- \frac{2}{x ^{3}} + \frac{36}{x ^{5}}) (x + 3 x^{3}) + (1 + 9 x^{2}) (\frac{1}{x ^{2}} - \frac{9}{x ^{4}}) : \frac{26}{x ^{2}} + \frac{27}{x ^{4}} + 3

= \frac{26}{x ^{2}} + \frac{27}{x ^{4}} + 3

\int_{- 2}^{2} 4 - x^{2} d x

\int_{0}^{3} 4 - x d x

y^{^{''}} + 2 y^{^{'}} + 14 y = 0, y (0) = 1, y^{^{'}} (0) = 0

f (x) = sin (3 x + 2)

\int \frac{1}{4 + x} d x