find the derivative of the function.\n$f(x)=\frac{x^{3}-3x^{2}+6}{x^{2}}\n$f(x)=$

find the derivative of the function.\n$f(x)=\frac{x^{3}-3x^{2}+6}{x^{2}}\n$f(x)=$

find the derivative of the function.\n$f(x)=\frac{x^{3}-3x^{2}+6}{x^{2}}\n$f(x)=$

Answer

Explanation:

Step1: Simplify the function

$f(x) = x - 3 + 6x^{-2}$

Step2: Differentiate term by term

$f'(x) = 1 + 0 + 6(-2)x^{-3}$

Step3: Simplify the result

$f'(x) = 1 - 12x^{-3}$

Answer:

$1 - \frac{12}{x^3}$