SultanOfSwing

I know, I just typed the wrong operator. WGAF?

MarylandNed

Here's the mathematical proof:

Differentiation is rate of change, which is basically the slope at a certain point in a graph. A straight line always has the same slope at any point on the line. However, not all graphs are straight lines in which case the slope is dependent on where you are on the graph. The slope at any point would be the slope of a tangent to the point.

Consider 2 points on the non-linear graph y=2x³:

(x, 2x³) and a point nearby (x+h, 2(x+h)³).

The slope of a straight line between the 2 points is the difference in y (delta y) divided by the difference in x (delta x)

delta y = 2(x+h)³ - 2x³ = 2x³ + 6x²h + 6xh² + 2h³ - 2x³ = 6x²h + 6xh² + 2h³

delta x = (x+h) - x = x + h - x = h

dividing delta y (=6x²h + 6xh² + 2h³) by delta x (=h) gives us the slope:

6x² + 6xh + 2h²

Now as h approaches 0 (i.e. the distance between the 2 points gets very small) you get closer to the real tangential slope at the point x.

So h=0, means that our tangential slope at the point x is:
6x² + 6xh + 2h² = 6x² + 6x(0) + 2(0)² = 6x²

Q.E.D.

Mr Weeze

You should be excluded from pedant of the year for this post.

SultanOfSwing

It was from ages ago. You have to get in right away, otherwise there's no point.

Anian

My daughter has been asking for help with her reading comprehension homework. Some of the questions are so vague you can't tell what they are asking for, others seem to ask for information that isn't in the given text. In all cases, she barely has space to write the answers. She is always frustrated by it. It seems to be an exercise in how to deal with complete nonsense - a skill required in most workplaces today.

Mr Weeze

No. It was from 9:22 today. I don't mean for the original error, but for the response to the error; for the WGAF. That is behaviour not becoming of a pedant.

SultanOfSwing

Meh.

steveq

WTF, multiply by the index, and drop it one down.

MarylandNed

Yes, but someone had to prove that rule first! That was done using limits as in the proof I posted. Unfortunately homework help didn't end for me at high school. I'm a physicist, mathematician and computer scientist. So I still get homework help calls from my kids at college.