SAT PrepWhat is the distance in space between the points with coordinates and ?

Basic Differentiation Rules and Rates of Change• Find the derivative of a function using the Constant Rule• Find the derivative of a function using the Power Rule• Find the derivative of a function using the Constant Multiple Rule• Find the derivative of a function using the Sum and Difference Rules• Find the derivative of the sine and of the cosine functions

• Use derivative to find rates of change

The Constant RuleThe derivative of a constant function is 0. That is, if is a real number, then

The Power RuleIf is a rational number, then the functionis differentiable andFor to be differentiable at , must be a number such that is defined on an interval containing 0.

𝑑𝑑𝑥

[𝑥4 ]

𝑑𝑑𝑥

[𝑥1/2 ]

The Constant Multiple RuleIf is a differentiable function and is a real number, then is also differentiable and

𝑑𝑑𝑥

[ 4 𝑥2 ]

𝑑𝑑𝑥 [ 43 𝑥 ]

The Sum and Difference RulesThe sum (or difference) of two differentiable functions and is itself differentiable. Moreover, the derivative of is the sum (or difference) of the derivatives of and . That is,

𝑑𝑑𝑥

[sin 𝑥 ]=¿

𝑑𝑑𝑥

[cos 𝑥 ]=¿

If we were to drop a baked potato off of the top of the school, its position from the ground can be modeled by the function . What function models the potato’s velocity? Acceleration?