Differentation Rules

The class this morning started off with test corrections, which I really don't want to revisit.

The rest of the class was new stuff from chapter 4. This chapter is about the rules of calculating the derivative of a function in a faster way than what we've been doing from the last chapters.

Linear Function Rule

ie) f(x) = x
As we know, the derivative is the slope of the function. So the derivative of a straight line would always be constant since the slope does not change. In this example the slope of the function is 1, so f prime =1 (derivative of a linear function is always its slope).

Constant Function Rule

Constant functions are functions like y=1, y=2, etc. The derivative of a constant function is always 0 since there is no change in the slope.

Power Function Rule

The faster way of finding the derivative of a function without having to take smaller and smaller numbers from both sides.

ie) f(x)=x²

The rule is to take the exponent and multiply it to the coefficent and to subtract 1 from the original exponent to get the new exponent. So in this case we'd get 2x.

One other new thing was the d/dx symbol. It means the derivative of a function with respect to x.

I think those were all the rules we had time to go over but there's more in the book. The last scribe for this cycle will be Justus.