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

Lösung

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

\frac{15}{x ^{2}} + \frac{6}{x ^{4}} + 8

Schritte zur Lösung

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

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

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

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

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

Vereinfache

(- \frac{2}{x ^{3}} + \frac{8}{x ^{5}}) (x + 8 x^{3}) + (1 + 24 x^{2}) (\frac{1}{x ^{2}} - \frac{2}{x ^{4}}) : \frac{15}{x ^{2}} + \frac{6}{x ^{4}} + 8

= \frac{15}{x ^{2}} + \frac{6}{x ^{4}} + 8

n = 1 \sum \infty (\frac{1}{2})^{\frac{1}{n}}

\int_{1}^{2} (x + \frac{1}{x})^{2} d x

\frac{\partial}{\partial y} (5 x^{2} - 3 x y + x yz)

x \to \infty lim (- 2 \cdot x)

a re a y = e^{- x}, x = 2, y = 1