Differentiation Rules

Derive the Derivative for f(x) = xⁿ

Derive the Product Rule

Derive the Quotient Rule

Derivatives of Absolute Values

Write as a piecewise function, separating the intervals that give positive values for the inside of the absolute value from those that give negative values.  Remember, the derivative is undefined where the curve makes sharp turns.

Now,

Higher Order Derivatives

Suppose  f(x) = 3x⁴

Then   f '(x) = 12x³

          f "(x) = 36x²

          f '''(x) = 72x

          f ⁽⁴⁾(x) = 72

         f ⁽⁵⁾(x) = 0

         f ⁽⁶⁾(x) = 0