Answer to Question #331682 in Calculus for Olga

Question #331682

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



1
Expert's answer
2022-04-22T02:45:47-0400

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


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