Exercises57 15. Critical thinking question: 13) Give a function that requires three applications of the chain rule to differentiate. Cost is directly proportional to the number of articles. Use the quotient rule to differentiate the functions below with respect to x (click on the green letters for the solutions). A good way to detect the chain rule is to read the problem aloud. The Intermediate Value Theorem63 3. (You do not need to simplify your final answers here.) Solution: This problem requires the chain rule. Graph Sketching and Max-Min Problems63 1. If not, explain why. Implicit di erentiation58 16. If f(x) = g(h(x)) then f0(x) = g0(h(x))h0(x). Questions And Answers Forum Toggle navigation Finding sign changes of a function65 5. 1. Questions 1. Chain Rule Questions With Explanation in pdf.visit for more Chain Rule Questions With Explanation to download in pdf format. Section 3: The Quotient Rule 10 Exercise 4. Increasing and decreasing functions66 6. 5(4 3+6 )( 4+3 2−2)4) (b. We must identify the functions g and h which we compose to get log(1 x2). Is there a function all of whose values are equal to each other? 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? A R s. x y d. Usually what follows Exercises60 Chapter 5. Each of the following problems requires more than one application of the chain rule. The chain rule for powers tells us how to differentiate a function raised to a power. Ex. Worksheet 2.6—The Chain Rule Short Answer Show all work, including rewriting the original problem in a more useful way. SOLUTION 12 : Differentiate . 1. Download Chain Rule MCQ Question Answer PDF. 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. In fact, this problem has three layers. 1. Tangent and Normal lines to a graph63 2. (More Articles, More Cost) We are nding the derivative of the logarithm of 1 x2; the of almost always means a chain rule. 13. Find the derivative of the following functions with respect to the independent variable. (a) y = u/v, if u = eax, and v = ebx (b) y = u/v, if u = x+1, and v = x−1 Exercise 5. Chain Rule MCQ Question with Answer Chain Rule MCQ with detailed explanation for interview, entrance and competitive exams. Explanation are given for understanding. The Chain Rule52 14. (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. Then differentiate the function. Problems 1. Calculus 12 Unit 3: Derivatives and Differentiation 2019/2020 1 Worksheet 3 – Chain rule Answer Keys Question 1 a. 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. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx 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)). Examples67 7. 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. If so, graph your answer. This rule is obtained from the chain rule by choosing u = f(x) above. 1004−2 (4 − 2)99 c. 1 … FACTS AND FORMULAE FOR CHAIN RULE QUESTIONS . ( Recall that , which makes ``the square'' the outer layer, NOT ``the cosine function''. • The quotient rule • The chain rule • Questions 2. 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