Math 22 Higher-Order Derivative

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Higher-Order Derivatives

 The "standard" derivative  is called the first derivative of . The derivative of  is the second derivative of, denoted by 
 By continuing this process, we obtain higher-order derivative of .

Note: The 3rd derivative of is . However, we simply denote the derivative as for

Example: Find the first four derivative of




It is better to rewrite


If is the position function, then is the velocity function and is the acceleration function.

Word-Problem Example: A ball is thrown upward from the top of a -foot cliff. The initial velocity of the ball is feet per second. The position function is where is measured in seconds. Find the height, velocity, and acceleration of the ball at

(Position function)
(Velocity function)
(Acceleration function)
So, when , from the functions above, we can have:

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