sinx
cosx
cosx
-sinx
tanx
sec2x
cscx
-cscxcotx
secx
secxtanx
cotx
-csc2x
What are you doing if you plug a point into a derivative?
Finding the slope of the tangent line at that point
Difference quotient
limit as h approaches 0 of (f(x+h) - f(x))/h
Question gives you point on the original function. What does that mean?
The tangent line of the original function (aka, f’(x) goes through this point. The slope of the tangent line is what you get when you plug in this point to the derivative function.
What is the significance of a y-value you get after plugging an x value into the tangent line?
It means that point is on the original function.