Looking for help on the first half, not the Marine Biology question. rce Booksh...• For the function f (x) = cot (x):• Rewrite f (x) as a composite function f (x) =g(h (x)).• How did you decide what g (x) and h (x) are?• Find f (x) using the Chain Rule and your decomposition g (h (x)).Find the derivatives of each of the following functions, telling me how you choose the rules you use, and showing your3.process. It might help to use the strategies shown in the videos to organize your work for multiple "chain links", especially ifthere are also other rules involved.f (x) = 3tan(5a)o y = sin* 2x cos 3x + sin 2xf (t) = et lu(3t)In the videos this week, we stated without proof that yis the derivative of y = In a, after conjecturing that thismight be the case based on the asymptotic behavior of the tangent lines as z- 0 and r - 0o. Use the Inverse FunctionTheorem, and the fact that y= e andy =In are inverses of each other, to show that this derivative is correct.In the videos this week, we used the Inverse Function Theorem to find the derivative of the arcsine (inverse sine) function.This included a process where we drew a triangle and rewrote the derivative using identities. Use a similar process toverify the derivatives of the arccosine and arctangent functions.Application - Marine BiologyYou are studying the impacts of rising sea levels on an estuary, and are modeling how the salinity of a particular area changeswith the tidal cycle. The salinity is also impacted seasonally by snowmelt increasing river flows, so measurements are oftentaken in early autumn for this particular area. The mixed-tide cycle on this part of the coast has a period of approximately 25Sign out8:07DELL

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rce Booksh. • For the function f (x) = cot (x): Rewrite f (x) as a composite function f (x) = g(h (x)). • How did you decide what g (x) and h (x) are? • Find f' (x) using the Chain Rule and your decomposition g (h (x)). • Find the derivatives of

rce Booksh. • For the function f (x) = cot (x): Rewrite f (x) as a composite function f (x) = g(h (x)). • How did you decide what g (x) and h (x) are? • Find f' (x) using the Chain Rule and your decomposition g (h (x)). • Find the derivatives of

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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