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

Lösung

ableitung von

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

\frac{14}{x ^{2}} + \frac{9}{x ^{4}} + 5

Schritte zur Lösung

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

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

= (- \frac{2}{x ^{3}} + \frac{12}{x ^{5}}) (x + 5 x^{3}) + (1 + 15 x^{2}) (\frac{1}{x ^{2}} - \frac{3}{x ^{4}})

Vereinfache

(- \frac{2}{x ^{3}} + \frac{12}{x ^{5}}) (x + 5 x^{3}) + (1 + 15 x^{2}) (\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) : \frac{14}{x ^{2}} + \frac{9}{x ^{4}} + 5

= \frac{14}{x ^{2}} + \frac{9}{x ^{4}} + 5

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

\int \frac{4 x ^{5} - 2 x + 3}{x ^{3}} d x

in v erse l a pl a ce e^{- 2 s} (\frac{1}{s - 9})

d er i v a t i v e y = (2 x + 1)^{\frac{2}{3}} (3 x - 4)^{\frac{1}{2}}

\frac{d}{d t} (e^{t} \cdot cos (t))