Tutorial ExerciseCalculate=dydxStep 1In the given equation y = 2x(3x² - 1) we have the product of two differentiable functions of x: 2x and (3x² − 1).Therefore, to differentiate we must first recall the Product Rule which states that if f and g are differentiable functions of x, then so is their product fg, and the following formula applies.dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)=Many like to remember that the derivative of a product is the derivative of the first function times the second function plus the first function times the derivative of the second function.g'(x)f'(x) · g(x) + f(x).derivative of first second first derivative of secondSimplify your answer. HINT [See Examples 1 and 2.]y =If f(x)=2x(3×² – 1)For the given equation y = 2x(3x² − 1), if we let f(x) = 2x and g(x) = 3x² – 1, then y = 2x(3x² − 1) = f(x) · g(x). In other words, we can define f(x) = 2x as the first function andg(x)3x²1 as the second function.d [f(x)g(x)dx-dyNote that since y is the product of two differentiable functions, we can use the product rule to find the derivative of y with respect to x ordx=As a precursor to using the product rule, complete the following statements.2x, then f'(x) ==If g(x) = 3x² - 1, then g'(x) =

Tutorial Exercise dy Calculate Simplify your answer. HINT [See Examples 1 and 2.] dx y = 2x(3x² - 1) Step 1 In the given equation y = 2x(3x² - 1) we have the product of two differentiable functions of x: 2x and (3x² - 1). Therefore, to differentiate we must first recall the Product Rule which states that if f and g are differentiable functions of x, then so is their product fg, and the following formula applies. [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Many like to remember that the derivative of a product is the derivative of the first function times the second function plus the first function times the derivative of the second function. g'(x) g(x) + f(x). [(x)9(x)] = f'(x) derivative of first second first derivative of second d dx For the given equation y = 2x(3x² - 1), if we let f(x) = 2x and g(x) = 3x² - 1, then y = 2x(3x2 - 1) = f(x) · g(x). In other words, we can define f(x) = 2x as the first function and g(x) = 3x²1 as the second function. dy Note that since y is the product of two differentiable functions, we can use the product rule to find the derivative of y with respect to x or dx As a precursor to using the product rule, complete the following statements. If f(x) = 2x, then f'(x) = If g(x)=3x21, then g'(x) =

Tutorial Exercise dy Calculate Simplify your answer. HINT [See Examples 1 and 2.] dx y = 2x(3x² - 1) Step 1 In the given equation y = 2x(3x² - 1) we have the product of two differentiable functions of x: 2x and (3x² - 1). Therefore, to differentiate we must first recall the Product Rule which states that if f and g are differentiable functions of x, then so is their product fg, and the following formula applies. [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Many like to remember that the derivative of a product is the derivative of the first function times the second function plus the first function times the derivative of the second function. g'(x) g(x) + f(x). [(x)9(x)] = f'(x) derivative of first second first derivative of second d dx For the given equation y = 2x(3x² - 1), if we let f(x) = 2x and g(x) = 3x² - 1, then y = 2x(3x2 - 1) = f(x) · g(x). In other words, we can define f(x) = 2x as the first function and g(x) = 3x²1 as the second function. dy Note that since y is the product of two differentiable functions, we can use the product rule to find the derivative of y with respect to x or dx As a precursor to using the product rule, complete the following statements. If f(x) = 2x, then f'(x) = If g(x)=3x21, then g'(x) =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Answer the question below: Let c be a differentiable function of a and b that satisfies the equation below. ab?c3 + cot(bc — а) — а + 2b + 3с The student should find:- ab
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PART ONE: f(x) = ab* ➤ In this part, you are going to explore the behavior of the function using various values of the parameters a & b. 1. When will the function have the following properties: x → ∞o, y → 0 Describe the parameters a & b that leads to the property above. Follow up: Print three functions of this type on one Cartesian Plane. Make sure to correctly label the functions. 2. When will the function have the following properties: x →∞o, y co Describe the parameters a & b that leads to the property above. Follow up: Print three functions of this type on one Cartesian Plane. Make sure to correctly label the functions. 3. The first two questions only covered the "two types". In fact, there are "four types" of f(x) = ab* in terms of "trend". You are tasked to explore the other two. TASK: Upon exploration, make a detailed summary of the relationships of the "four types".
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6. A small company can employ 3 workers. Each worker independently stays on the job for an exponentially distributed time with a mean of one year and then quits. When a worker quits, it takes the company an exponentially distributed time with a mean of 1/10 of a year to hire a replacement for that worker (independently of how long it takes to replace other workers). If the company takes in $1000 per day in revenue when it has 3 workers, $800 per day when it has 2 workers, and $500 per day when it has 0 or 1 workers, what is the company's long-run average daily revenue?
NASA launches a rocket at t O seconds. Its height, in meters above sea-level, as a function of time is given by h(t) 4.9t2 + 103t + 325. - Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level. Question Help: DVideo 1 DVideo 2
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