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. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx A good way to detect the chain rule is to read the problem aloud. 5(4 3+6 )( 4+3 2−2)4) (b. SOLUTION 12 : Differentiate . We are nding the derivative of the logarithm of 1 x2; the of almost always means a chain rule. If not, explain why. Usually what follows Critical thinking question: 13) Give a function that requires three applications of the chain rule to differentiate. 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. Then differentiate the function. Section 3: The Quotient Rule 10 Exercise 4. Is there a function all of whose values are equal to each other? • The quotient rule • The chain rule • Questions 2. Questions 1. Solution: This problem requires the chain rule. Explanation are given for understanding. 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) y = u/v, if u = eax, and v = ebx (b) y = u/v, if u = x+1, and v = x−1 Exercise 5. ( Recall that , which makes ``the square'' the outer layer, NOT ``the cosine function''. (You do not need to simplify your final answers here.) Increasing and decreasing functions66 6. A R s. x y d. Implicit di erentiation58 16. We must identify the functions g and h which we compose to get log(1 x2). 13. Chain Rule Questions With Explanation in pdf.visit for more Chain Rule Questions With Explanation to download in pdf format. 1. Cost is directly proportional to the number of articles. However, all you need to remember Ex. Tangent and Normal lines to a graph63 2. The Chain Rule52 14. Use the quotient rule to diﬀerentiate the following with Calculus 12 Unit 3: Derivatives and Differentiation 2019/2020 1 Worksheet 3 – Chain rule Answer Keys Question 1 a. 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). 1. Examples67 7. FACTS AND FORMULAE FOR CHAIN RULE QUESTIONS . Download Chain Rule MCQ Question Answer PDF. Exercises60 Chapter 5. Find the derivative of the following functions with respect to the independent variable. Maxima and Minima69 8. (More Articles, More Cost) If f(x) = g(h(x)) then f0(x) = g0(h(x))h0(x). Finding sign changes of a function65 5. In fact, this problem has three layers. The chain rule for powers tells us how to diﬀerentiate a function raised to a power. No calculator unless otherwise stated. Chain Rule MCQ Question with Answer Chain Rule MCQ with detailed explanation for interview, entrance and competitive exams. Problems 1. The Intermediate Value Theorem63 3. Two version of the chain rule are shown above. 1004−2 (4 − 2)99 c. 1 … 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. Graph Sketching and Max-Min Problems63 1. Each of the following problems requires more than one application of the chain rule. Exercises64 4. (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. 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)). 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