Differentiation - power functions

To differentiate a power function y = axⁿ :

• multiply by the index
• reduce the index by 1.

Remember the special case of a linear function which has the same gradient at every point on the graph.

• The derivative of  y = mx  is m.
• The derivative of  y = c  is 0.
• The derivative of  y = mx + c  is m.

To differentiate a polynomial function (e.g.  y = 5x³ + 4x² - 7x + 9):

• Differentiate each term separately. (The derivative is 15x² +8x - 7.)

A more formal approach to the derivative and the differentiation rules is provided by Visual Calculus.