I am struggling understanding how to differentiate negative indices. I get confused with the power increasing or decreasing.

Hi there, this is a common confusion so don't worry.
It is helpful to write out a number line when differentiating and drawing an arrow to show which way the power is moving.
<---- differentiate----3 -2 -1 0 1 2 3
For example:
Given y = 4x² + 3x^-1
Find dy/dx:
First term: dy/dx = (4 x 2) x¹ = 8x
Second term: dy/dx = (3 x -1) x^-2 = -3x^-2 use your number line remind you to subtract 1 from -1 to give -2
Combine: dy/dx = 8x - 3x^-2