Derivative Rules 3.3.

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3.3 Differentiation Rules

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Presentation transcript:

Derivative Rules 3.3

Derivative of a Constant For any constant C, Suppose f(x) is a constant function, that is, f(x) = C, where C is a constant. Since the value of the function never changes, the instantaneous rate of change must be zero. Examples:

Derivatives of Powers Derivative of a Power Examples: If n is any real number (n may or may not be an integer), Another way to remember this rule is “power in front, reduce the power by one”. Examples:

constant multiple rule: examples:

constant multiple rule: sum and difference rules: (Each term is treated separately)

Derivatives of trig functions

Example: Find the derivative of:

Example: Find the derivative of:

Example: Find the derivative of:

Example: Find the derivative of:

Example: Find the horizontal tangents of: Horizontal tangents occur when slope = zero. Plugging the x values into the original equation, we get: (The function is even, so we only get two horizontal tangents.)

Higher Order Derivatives 2nd derivative 3rd derivative 1st derivative

Find the first 4 derivatives of:

Find the derivative of: We have to foil first!

Find the slope of the curve y = 2cos(x) at: