y=e^(2x) - x^3. Find dy/dx. (please note this is "e to the power of 2x, minus x cubed")

The rules to know are 1) when differentiating e to the power of x... be it 2x or 100x... you bring down the number in front of x, and leave the power as it is. in our case e^(2x) goes to 2e^(2x).

2. When differentiating x to the power of something, bring the power down (here is 3) and decrease the power by one. So -x^3 goes to -3x^2. Note the minus stays for the ride all the way from the question.

Our final answer is dy/dx = 2e^(2x) -3x^2. (said as two e to the power of 2x, minus 3x squared)