Unit 2 AP Calc AB Derivatives

How to find derivative on calculator (make sure it is in radians): 1. MATH -> 2. 8:nDeriv( -> 3. input function, variable, and value of x (if you're using TI-84 plus w/o color, input nDeriv(function, variable,

Derivative (instantaneous rate of change) at x=a as h approaches 0

Derivative (instantaneous rate of change) at x=a as x approaches a number

Equation of a tangent line formula

Average rate of change of a function over an interval without h

Average rate of change of a function over an interval with h

The derivative fails to exist where the function has a:

1. Hole or Jump

2. Vertical Asymptote

3. Corner or Cusp

Differentiability implies continuity

True

Continuity implies differentiability

False; a counter example would include a corner or a cusp

Power rule

Derivative for a constant

Derivative for a constant multiple

Derivative for a sum/difference

Steps for finding the equation of a derivative

1. Point (a,b)

2. Slope (find derivative, then plug x-value into derivative)

3. Equation ( y - f(a) = f ’(a) ( x - a ) )

Normal line

Goes through same point as tangent line does but is perpendicular to tangent line. Slope is reciprocal of tangent’s slope

Steps to find if x=? is differentiable when given a piecewise function

1. Determine continuity: Find limits as x approaches ? from both sides by plugging in x → equal = continuous

2. Determine differentiability: Find derivatives of limits as x approaches from both sides and plug in x → equal = differentiable

Derivative of cosx

Derivative of sinx

Product rule

Quotient rule

Derivative of tanx

Derivative of cotx

Derivative of secx

Derivative of cscx