Answer to Question #331682 in Calculus for Olga

Question

Differentiate the function:

.F(x)= x − 4x^2 / x^3.

is

a. F′(x)= 2 / x^3 − 4 / x^2

b.F′(x)= 3x^2 − 24x

c.F′(x)= − 2 / x^3 + 4 / x^2

d.F′(x)= 1 − 8x / 3x^2

Answer 1

$F(x) =\cfrac{x-4x^2}{x^3}\\ F'(x) = \cfrac{(1-8x)x^3 - 3x^2(x-4x^2)}{x^6} = \\ =\cfrac{x^3 -8x^4 -3x^3 +12x^4}{x^6}=\\ = \cfrac{4x^4 -2x^3}{x^6} = \cfrac{4x-2}{x^3} =-\cfrac{2}{x^3} +\cfrac{4}{x^2}$ So answer is C