chain rule questions and answers pdf

Questions 1. Calculus 12 Unit 3: Derivatives and Differentiation 2019/2020 1 Worksheet 3 – Chain rule Answer Keys Question 1 a. If f(x) = g(h(x)) then f0(x) = g0(h(x))h0(x). Graph Sketching and Max-Min Problems63 1. 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. The Chain Rule52 14. 1004−2 (4 − 2)99 c. 1 … Maxima and Minima69 8. SOLUTION 12 : Differentiate . Exercises57 15. We must identify the functions g and h which we compose to get log(1 x2). However, all you need to remember 13. ( Recall that , which makes ``the square'' the outer layer, NOT ``the cosine function''. Exercises60 Chapter 5. We are nding the derivative of the logarithm of 1 x2; the of almost always means a chain rule. 1. A R s. x y d. 5(4 3+6 )( 4+3 2−2)4) (b. 1. 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)). Worksheet 2.6—The Chain Rule Short Answer Show all work, including rewriting the original problem in a more useful way. FACTS AND FORMULAE FOR CHAIN RULE QUESTIONS . Problems 1. A good way to detect the chain rule is to read the problem aloud. Then differentiate the function. Section 3: The Quotient Rule 10 Exercise 4. Download Chain Rule MCQ Question Answer PDF. No calculator unless otherwise stated. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx Finding sign changes of a function65 5. Tangent and Normal lines to a graph63 2. Questions And Answers Forum Toggle navigation The chain rule for powers tells us how to differentiate a function raised to a power. Ex. • The quotient rule • The chain rule • Questions 2. (More Articles, More Cost) Chain Rule Questions With Explanation in pdf.visit for more Chain Rule Questions With Explanation to download in pdf format. Implicit di erentiation58 16. Use the quotient rule to differentiate the functions below with respect to x (click on the green letters for the solutions). (a) y = u/v, if u = eax, and v = ebx (b) y = u/v, if u = x+1, and v = x−1 Exercise 5. Exercises64 4. Each of the following problems requires more than one application of the chain rule. The Intermediate Value Theorem63 3. 1. In fact, this problem has three layers. Two version of the chain rule are shown above. Increasing and decreasing functions66 6. Find the derivative of the following functions with respect to the independent variable. 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. Solution: This problem requires the chain rule. Explanation are given for understanding. Examples67 7. The first layer is ``the square'', the second layer is ``the cosine function'', and the third layer is . 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. (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. (You do not need to simplify your final answers here.) Critical thinking question: 13) Give a function that requires three applications of the chain rule to differentiate. Chain Rule MCQ Question with Answer Chain Rule MCQ with detailed explanation for interview, entrance and competitive exams. Use the quotient rule to differentiate the following with If not, explain why. This rule is obtained from the chain rule by choosing u = f(x) above. Cost is directly proportional to the number of articles. 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