Find the horizontal tangents of the curve:

The lesson is about shortcut rules for derivatives.

Rules such as:

Power rule-

Power Rule of positive integer- same

Power Rule of negative integers- same

Product rule- derivative of (uv) = derivative of u + derivative of v

Constant function rule - derivative of any integer is 0

Quotient rule- don't know how to LaTex or describe. Don't need for this though.

I simplified the function to

.

I know the goal of horizontal tangents is to get 0 = 0

Answers I got: x= 0

There should be more, as that is the pattern of other problems.

Is there any way to figure it out algebraically? I'm very bad at trial and error. I found nothing else.