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

Lösung

ableitung von

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

\frac{26}{x ^{2}} + \frac{9}{x ^{4}} + 9

Schritte zur Lösung

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

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

\frac{d}{d x} (\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) = - \frac{2}{x ^{3}} + \frac{12}{x ^{5}}

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

= (- \frac{2}{x ^{3}} + \frac{12}{x ^{5}}) (x + 9 x^{3}) + (1 + 27 x^{2}) (\frac{1}{x ^{2}} - \frac{3}{x ^{4}})

Vereinfache

(- \frac{2}{x ^{3}} + \frac{12}{x ^{5}}) (x + 9 x^{3}) + (1 + 27 x^{2}) (\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) : \frac{26}{x ^{2}} + \frac{9}{x ^{4}} + 9

= \frac{26}{x ^{2}} + \frac{9}{x ^{4}} + 9

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

\frac{d ^{2} y}{d t ^{2}} + 10 \frac{d y}{d t} + 25 y = 0

\frac{d}{d x} (\frac{x ^{3} y + x y ^{3}}{x ^{2} + y ^{2}})

t an g e n t f (x) = x - 4, (13, 3)

t an g e n t f (x) = \frac{5}{x + 1}, at x = \frac{- 1}{3}