derivative f(x)=(4-x)(2/(x^2)-3)

Lösung

ableitung von

f (x) = (4 - x) (\frac{2}{x ^{2}} - 3)

\frac{2 x - 16}{x ^{3}} + 3

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 4 - x, g = \frac{2}{x ^{2}} - 3

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

\frac{d}{d x} (4 - x) = - 1

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

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

Vereinfache

(- 1) (\frac{2}{x ^{2}} - 3) + (- \frac{4}{x ^{3}}) (4 - x) : \frac{2 x - 16}{x ^{3}} + 3

= \frac{2 x - 16}{x ^{3}} + 3

t an g e n t y = - e^{- x - 2}, (- 3, - e)

\frac{\partial}{\partial v} (v)

\frac{d}{d x} (x + y)

x \to 3 lim (\frac{x ^{3} - 9 x}{( x ^{2} ) - 3 x})

x \to \frac{3}{2} lim (x)