(4x^3-2x+1)/x^2, find the f'(x) of this

To find the derivative of the function f(x) = (4x^3 - 2x + 1) / x^2, we can first simplify the function by dividing each term by x^2. This gives us:

f(x) = 4x - 2/x + 1/x^2

Now we can find the derivative of each term separately.

The derivative of 4x with respect to x is 4.

The derivative of -2/x with respect to x is 2/x^2. This is because the derivative of 1/x is -1/x^2, so when we multiply by -2, we get 2/x^2.

The derivative of 1/x^2 with respect to x is -2/x^3. This is because the derivative of 1/x^n is -n/x^(n+1), so when n=2, we get -2/x^3.

So the derivative of the function f(x) = (4x^3 - 2x + 1) / x^2 is:

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