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