only problem 4. I would like to compare my results. Problem 1. Calculate the derivatives of the following functions. Show all of your work andclearly indicate any derivative rules that you use. Do not simplify your answers.Let b denote the last nonzero digit of your UCID number, that is, if your UCID numberis 9876543210 then b = 1..2(1) ƒ(x) = (2x + b)(e"¨+sin(ba))%3D(2) g(x) = tan-1(tan(bx)+sin-'(bx))Note: tan-(x) = arctan(x) + e = cot(r).1tan(x)|(3) If g(x) is differentiable, find f'(x) where f(x) = g(x+b) cos-(x³).%3DProblem 2. In the following, use implicit differentiation.dy(1) If e – cos-y) = x, finddxdythen findd.x(2) If x sec(y)tan(x)'dy(3) If x + xy + y? = 3, then find the second derivative y"%3Ddx?Problem 3. Let b denote the last nonzero digit of your UCID number, that is, if your UCIDnumber is 9876543210 then b = 1.If y = (x+ b)+b, find y'.Problem 4. If h(x) = 5(f(x))²+g(x)], where we know that f is one-to-one and%3Df'(2) = -1g'(2) = 7f'(3) = 11g'(4) = -3,f(2) = 3f(3) = 4%3D%3D%3Dg(2) = 4g(4) = 3then find h'(2) and (f-1)'(3).Problem 5. Consider the curve r = sin(y). Find the point on the curve where the tangent%3Dline is parallel to the line y = -x and such that the y-coordinate of the point is (are) between0< U< 2T) Thore may be one or more such points.%3D0.and 2r (i o

Answered: Problem 4. If h(x) = 5 ()+g(x)), where…

Problem 4. If h(x) = 5 ()+g(x)), where we know that f is one-to-one and f(2) = 3 f(3) = 4 f'(2) = -1 f'(3) = 11 g'(4) = -3, %3D %3D %3D g(2) = 4 g(4) = 3 g'(2) = 7 %3D then find h'(2) and (f-1)'(3).

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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