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 uses of 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