To derive this function, we'll only need the power rule.
Power rule is expressed with the following function:

We can derive each of the terms individually. Rewrite the problem:
![(d)/(dx) [(1)/(√(x)) - 3.2x^(-2) + x] = ((d)/(dx) (1)/(√(x))) - ((d)/(dx) 3.2x^(-2)) + ((d)/(dx) x)](https://img.qammunity.org/2019/formulas/mathematics/college/vrqlfnc7zsmjkkdx3h9smbgjw8zk3yw0hz.png)
For the first term, we'll rewrite the term, then use the power rule (note that square roots can be rewritten as any number to the 1/2 power):

For the second term, we'll use power rule:

The third term is simple:

The equation should now look like this, and result in your answer:
![(d)/(dx) [(1)/(√(x)) - 3.2x^(-2) + x] = -\frac{1}{2x^{(3)/(2)}} - (-(32)/(5x^3)) + 1 = \boxed{-\frac{1}{2x^{(3)/(2)}} + (32)/(5x^3) + 1}](https://img.qammunity.org/2019/formulas/mathematics/college/hssat5ctiw2okm06qyfrha1889ewv9wbln.png)