1. 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? Maxima and Minima69 8. 1004−2 (4 − 2)99 c. 1 … 1. The chain rule for powers tells us how to differentiate a function raised to a power. Download Chain Rule MCQ Question Answer PDF. The Chain Rule52 14. Exercises60 Chapter 5. (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. Explanation are given for understanding. (You do not need to simplify your final answers here.) Examples67 7. ( Recall that , which makes ``the square'' the outer layer, NOT ``the cosine function''. 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. Usually what follows FACTS AND FORMULAE FOR CHAIN RULE QUESTIONS . Finding sign changes of a function65 5. We are nding the derivative of the logarithm of 1 x2; the of almost always means a chain rule. If f(x) = g(h(x)) then f0(x) = g0(h(x))h0(x). Use the quotient rule to differentiate the functions below with respect to x (click on the green letters for the solutions). Chain Rule MCQ Question with Answer Chain Rule MCQ with detailed explanation for interview, entrance and competitive exams. Find the derivative of the following functions with respect to the independent variable. 13. 5(4 3+6 )( 4+3 2−2)4) (b. Critical thinking question: 13) Give a function that requires three applications of the chain rule to differentiate. 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. Questions 1. Then differentiate the function. This rule is obtained from the chain rule by choosing u = f(x) above. Implicit di erentiation58 16. Worksheet 2.6—The Chain Rule Short Answer Show all work, including rewriting the original problem in a more useful way. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx 1. Calculus 12 Unit 3: Derivatives and Differentiation 2019/2020 1 Worksheet 3 – Chain rule Answer Keys Question 1 a. However, all you need to remember A good way to detect the chain rule is to read the problem aloud. We must identify the functions g and h which we compose to get log(1 x2). (More Articles, More Cost) If not, explain why. Exercises57 15. 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)). Section 3: The Quotient Rule 10 Exercise 4. 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. Tangent and Normal lines to a graph63 2. Solution: This problem requires the chain rule. In fact, this problem has three layers. Use the quotient rule to differentiate the following with Ex. No calculator unless otherwise stated. • The quotient rule • The chain rule • Questions 2. Is there a function all of whose values are equal to each other? Increasing and decreasing functions66 6. Graph Sketching and Max-Min Problems63 1. A R s. x y d. Cost is directly proportional to the number of articles. 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. Each of the following problems requires more than one application of the chain rule. Problems 1. (a) y = u/v, if u = eax, and v = ebx (b) y = u/v, if u = x+1, and v = x−1 Exercise 5. SOLUTION 12 : Differentiate . 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 . 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