can you explain the whole process, step-by-step? like in an essay type. how did they find the first and second derivatives?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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can you explain the whole process, step-by-step? like in an essay type. how did they find the first and second derivatives?
Solution :-
we have
Fla) =5 cas 2x
%3D
Now
di'fferentiate it wot x
x d (cos2x)
* (-2sin2a)
%3D
f'ca)
-Sin 2x
First deri'vVative
- Sin 2x . Ang
f'(x)
-Sin 22
And
Now , differ entiate it wat x
p"(x) =
-2 Cos2x
%3D
So, Second derivative is -2 Cos2x d
Transcribed Image Text:Solution :- we have Fla) =5 cas 2x %3D Now di'fferentiate it wot x x d (cos2x) * (-2sin2a) %3D f'ca) -Sin 2x First deri'vVative - Sin 2x . Ang f'(x) -Sin 22 And Now , differ entiate it wat x p"(x) = -2 Cos2x %3D So, Second derivative is -2 Cos2x d
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