Differentiating every function from first principles would be very time consuming and you will be glad to know that that is not what you will be doing! We will instead have a table of basic building blocks and then rules by which we can use these to find the derivatives of many functions. Rather than finding all of the building blocks from first principles (we'll leave that to the mathematicians) we instead want to reassure ourselves that we believe the results!
Use the Geogebra worksheet to collect evidence that supports the conclusion that the derivative of x^n is nx^{n-1}. You can re-define the function you are considering by typing, for instance, f(x)=x^3 into the input bar and then pressing ctrl-f to remove any of the trace from the old function. The refresh button restores the original function f.
What is the derivative of a constant function?
What are the derivatives of \sin x, \cos x, \ln x and e^x? Work through the whole process for each, try to work out what pattern tracing the slope as a function makes before you display the answer - if you can think it through you are more likely to remember it or be able to think it through again.
