dxdy​ is the rate of change of y with respect to x. That is, dxdy​ tells us how much y changes in response to a change in x.

If y=f(x), then dxdy​=f′(x).

The IB may test your understanding of the gradient of the curve as the limit of

as (x2​−x1​) goes to zero.

For a curve y=f(x), f′(x) is the gradient or slope.

You can graph f′(x) using the following steps:

• Press the Y= key.

• In one of the available function lines (e.g. Y_1), enter the expression for f(x).

• In another available line (e.g. Y_2), input the derivative function usingMATH then 8:nDeriv( in the following format:

  dXd​(Y1​(x))∣X=X​

  
  

• To enter Y1​, press VARS then scroll to Y-VARS and select FUNCTION then Y1​.

• Press GRAPH to display both the original graph f and the derivative f′.

• The graph of f′ may take a little bit longer depending on the original function.

After graphing f′, you may use all the other graphing functions on the calculator (intersect, zero, and value).

The limit x→alim​f(x) is the value f(x) approaches as x approaches a.

Given a table of values: