AP Calc AB

:(

cos(2x)

• cos²x - sin²x

• 2cos²x -1

• 1 - 2sin²x

sin(2x)

2sin(x)cos(x)

d/dx tan(x)

sec²x

d/dx cot(x)

-csc²x

d/dx sec(x)

sec(x)tan(x)

d/dx csc(x)

-csc(x)cot(x)

first derivative

• y’

• f’(x)

• d/dx[f(x)]

• dy/dx

second derivative

• y’’

• f’’(x)

• d²/dx²[f(x)]

• d²y/dx²

third derivative

• y’’’

• f’’’(x)

• d³/dx³[f(x)]

• d³y/dx³

fourth derivative

• y⁽⁴⁾

• f⁽⁴⁾(x)

• d⁴/dx⁴[f(x)]

• d⁴y/dx⁴

Average velocity

The total change in position (displacement) divided by the total change in time

Instantaneous velocity

The derivative of the positive function at a certain point

Speed

the absolute value of velocity

Acceleration

The rate of change in velocity (the derivative of velocity)

When is the object speeding up?

When a(t) and v(t) have the same sign

When is the object slowing down?

When a(t) and v(t) have different signs

Total distance traveled on [a, b] with a change of direction at t = c

| s(a) - s(c) | + | s(c) - s(b) |

Displacement on [a, b]

s(b) - s(a)