Question No : 1 If the cost of X metres of wire is d rupees,then what is the cost of y metres of wire at the same rate? 1. Exercises64 4. Examples67 7. VCE Maths Methods - Chain, Product & Quotient Rules The chain rule 3 • The chain rule is used to di!erentiate a function that has a function within it. The Intermediate Value Theorem63 3. It states: if y = (f(x))n, then dy dx = nf0(x)(f(x))n−1 where f0(x) is the derivative of f(x) with respect to x. Direct Proportion: Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent. (a) y = u/v, if u = eax, and v = ebx (b) y = u/v, if u = x+1, and v = x−1 Exercise 5. The chain rule enables us to answer this question without actually ever having to calculate z as an explicit function of u and v. It is usually much more effective to use the chain rule than to calculate the new function w (u,v) = z (x (u,v),y (u,v)). ( Recall that , which makes ``the square'' the outer layer, NOT ``the cosine function''. Calculus 12 Unit 3: Derivatives and Differentiation 2019/2020 1 Worksheet 3 – Chain rule Answer Keys Question 1 a. Questions 1. A good way to detect the chain rule is to read the problem aloud. Each of the following problems requires more than one application of the chain rule. Use the quotient rule to diﬀerentiate the following with (a) Find all x such that f(x) ≤ 2 where f(x) = −x2 +1 f(x) = (x−1)2 f(x) = x3 Write your answers in interval notation and draw them on the graphs of the functions. We must identify the functions g and h which we compose to get log(1 x2). 1004−2 (4 − 2)99 c. 1 … 1. We are nding the derivative of the logarithm of 1 x2; the of almost always means a chain rule. 13. 5(4 3+6 )( 4+3 2−2)4) (b. In fact, this problem has three layers. Ex. Questions And Answers Forum Toggle navigation A R s. x y d. However, all you need to remember Solution: This problem requires the chain rule. • The quotient rule • The chain rule • Questions 2. Cost is directly proportional to the number of articles. Explanation are given for understanding. Usually what follows Increasing and decreasing functions66 6. Exercises60 Chapter 5. Is there a function all of whose values are equal to each other? (More Articles, More Cost) Find the derivative of the following functions with respect to the independent variable. The chain rule for powers tells us how to diﬀerentiate a function raised to a power. Maxima and Minima69 8. Chain Rule MCQ Question with Answer Chain Rule MCQ with detailed explanation for interview, entrance and competitive exams. Problems 1. Worksheet 2.6—The Chain Rule Short Answer Show all work, including rewriting the original problem in a more useful way. Use the quotient rule to diﬀerentiate the functions below with respect to x (click on the green letters for the solutions). Implicit di erentiation58 16. No calculator unless otherwise stated. Tangent and Normal lines to a graph63 2. Then differentiate the function. Download Chain Rule MCQ Question Answer PDF. Finding sign changes of a function65 5. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx Exercises57 15. Section 3: The Quotient Rule 10 Exercise 4. (You do not need to simplify your final answers here.) Graph Sketching and Max-Min Problems63 1. Two version of the chain rule are shown above. The first layer is ``the square'', the second layer is ``the cosine function'', and the third layer is . Chain Rule Questions With Explanation in pdf.visit for more Chain Rule Questions With Explanation to download in pdf format. If so, graph your answer. Critical thinking question: 13) Give a function that requires three applications of the chain rule to differentiate. If f(x) = g(h(x)) then f0(x) = g0(h(x))h0(x). SOLUTION 12 : Differentiate . 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