Maple worksheets on derivatives |

Basic calculus topics:

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Derivatives from first principles-deriv1.mws

- The derivatives or gradient function associated with a function f(x).
- The standard limit formula for the derivative of a function.
- Examples of determining derivatives from first principles.
- Examples of derivatives of functions of the form f(x)=x^r.
- The formula for the derivatives of a function of the form f(x)=x^r.
- More examples of determining derivatives of functions from first principles.

A procedure which performs differentiation from first principles-deriv2.mws

- A procedure for showing the steps of differentiation from1st principles:
diffbylimit.- Examples of the form: d/dx [x^r].
- Examples of the form: d/dx [q(x)] where q(x) is a polynomial or rational function of x.
- Examples of the form: d/dx [q(x)^r] where q(x) is a polynomial or rational function of x.

Graphs of derivatives-drvgrph.mws

- Graphs of derivatives.
- An animation procedure for graphs of derivatives:
derivplot.- Tangents which meet a curve at another point.

The power rule, linearity of differentiation and Leibniz notation-rules1.mws

- The power rule for differentiation.
- The sum rule for differentiation.
- The restricted rule for multiplication by a constant.
- Leibniz notation.
- Setting up a Maple procedure to perform differentiation.
- The Maple procedure:
diff.- The differential operator
D.

More differentiation rules-rules2.mws

- The chain rule for differentiation.
- The product rule for differentiation.
- The quotient rule for differentiation.

Tangent and normal lines to curves-tangents.mws

- The point-slope equation of a line.
- Perpendicular lines and the normal line to a curve at a point.
- Examples of finding equations of tangent and normal lines to curves.
- Tangents which meet a curve at another point.

The meaning and usesof the derivative of a function-changes.mws

- The derivative and small changes.
- Average and instantaneous rates of change.
- An example to introduce the notions of differentiability and non-differentiability of a function.

Geometrical interpretation of derivatives-statpts.mws

- Stationary points.
- Comparison of graphs of function and derivative.

Calculus procedures-calculus.zip