# SurCalCh2Sec5 - after each derivative This makes taking...

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Survey Calculus 2.5, Higher-Order Derivatives Notation: First Derivative ) ( ' x f ) ( x f dx d ' y dx dy Second Derivative ) ( ' ' x f ) ( 2 2 x f dx d ' ' y 2 2 dx y d Third Derivative ) ( ' ' ' x f ) ( 3 3 x f dx d ' ' ' y 3 3 dx y d Nth Derivative ( ) ( ) x f n ) ( x f dx d n n ( ) n y n n dx y d To take the second derivative of a function, you first take the first derivative. The second derivative is the derivative of that. The third derivative is the derivative of the second derivative and so on and so forth. It is generally a good idea to simplify
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Unformatted text preview: after each derivative. This makes taking subsequent derivatives simpler. #4 #10 #16 #24 If gives distance from a starting point at time t, then at time t (velocity is another way to say instantaneous rate of change). Furthermore, or acceleration is the second derivative of the distance function. ) ( t s velocity t s = ) ( ' ) ( ) t a = ( ' ) ( ' ' t v t s = Example: #36...
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