The Derivative. Definition Example (1) Find the derivative of f(x) = 4 at any point x.

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Presentation transcript:

The Derivative

Definition

Example (1) Find the derivative of f(x) = 4 at any point x

Example (2) Find the derivative of f(x) = 4x at any point x

Example (3) Find the derivative of f(x) = x 2 at any point x

Example (4) Find the derivative of f(x) = x 3 at any point x

Example (5) Find the derivative of f(x) = x 4 at any point x

Power Rule Let: f(x) = x n, where n is a real number other than zero Then: f'(x ) = n x n-1 If f(x) = constant, then f ' (x) = 0

Algebra of Derivatives

Example (1)

Solution

The Chain Rule The derivative of composite function for the case f(x) = g n (x) Let: f(x) = g n (x) Then: f ' (x) = ng n-1 (x). g ' (x) Example: Let f(x) = (3x 8 - 5x + 3 ) 20 Then f(x) = 20 (3x 8 - 5x + 3 ) 19 (24x 7 - 5)

Exercises

Homework