Originally Posted by

**AllanCuz** This is good mate. Hard problems come from first principles, so a firm grasp of the basics is key!

What is a slope? Well a slope is simply rise over run. Think of it as elevation. So say we have a function and we want to know the instantaneous speed at a specific point. This means that we want the slope at that specific point.

Again, this is simply Rise over Run. However, with the derivation of derivatives we know this as the rate of change in the rise over the rate of change in the run. So essentially, we have the rate of change of the rise with respect to the run.

So it can then be said, we want to know how fast we are climbing (rise) with respect to how fast we are moving horizontally (run)

Does that clear it up at all?