Answering a question on the discussion board for calculus.

Anyone want to know how to do some calculus? Someone asked about this problem (section 2.3 #93) and here's my answer to it:

Here's the problem with more steps than what's in the solutions manual. Here's exactly what I did:

Here's the function, and what they want you to find with the function. Delta x, or the triangle next to x, means "change in x" - but we don't need to worry about that for now, just treat it as another variable.

Here is what it looks like when you set up the problem to begin with. f(x + Δx) is treated like f(x) in the sense that you use x + Δx instead of x when you're working it out.

Now, in the numerator (everything over Δx), you have to make the denomenators equal. Multiply each side of the subtraction sign by 1 using the other side's denomenator over itself. For example, the left side is multiplied by (x+3)/(x+3).

I took Δx out from under the rest, choosing to multiply everything that was in the numerator (what was over Δx) by 1/Δx, which is the same thing as dividing by Δx.

This is what it looks like after you simplify everything and multiply it together.

The Δx over Δx in the problem is just 1, so simplify it to that. Next, simply plug in 0 for Δx and you'll have your solution.