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L probiomio, 11j uppreciate ule sigtiliHcance ol chain rule in finding the d of a composite function. Learning Task 1: For the given functions f(x) and g(x), find (fo g)(x) 1. f(z) = x2 and g(x) =x+5 2. f(x) = x+1and g(x) = 4x2 -3 3. f(x) = x3 and g(x) = X-1 %3D 4. f(x) = sin x and g(x) = 2x 5. f(z) = x² + cosx and g(x) = 3x+ 4 Guide Questions: 1. How did you calculate (f e g)(x) ? 2. Is the result of the composition simpler or more complex that the comE functions?

L probiomio, 11j uppreciate ule sigtiliHcance ol chain rule in finding the d of a composite function. Learning Task 1: For the given functions f(x) and g(x), find (fo g)(x) 1. f(z) = x2 and g(x) =x+5 2. f(x) = x+1and g(x) = 4x2 -3 3. f(x) = x3 and g(x) = X-1 %3D 4. f(x) = sin x and g(x) = 2x 5. f(z) = x² + cosx and g(x) = 3x+ 4 Guide Questions: 1. How did you calculate (f e g)(x) ? 2. Is the result of the composition simpler or more complex that the comE functions?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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L probioiU, 1j uppreciate the siglncance ol chain rule in finding the derivative of a composite function. Learning Task 1: For the given functions f(x) and 9(x), find (fog)(x) 1. f(x) = x2 and g(x) = x+5 2. f(x) = x +1and g(x) = 4x2 -3 %3D 3. f(x) = x3 and g(x) x-1 4. f(x) = sin xand g(r) = 2x %3D 5. f(x) = x2 +cosx and g(x) = 3x+ 4 Guide Questions: 1. How did you calculate (fo g)(x) ? 2. Is the result of the composition simpler or more complex that the combined functions? Learning Task 2: Expand each function (using the appropriate technique/ formula). Compute the derivative of the expanded function by applying the differ- entiation rules. 1. flx) = (x + 5)2 2. f(x) = (4x2 – 3)2 3. f() = (x2 + 2x + 3)2 4. f(x) = (3x - 2)3 5. f(x) = sin (2x) %3! Derivative of Composite Functions and the Chain Rule Given the problem find the derivative of G) = (4x - 3)a how will you do it? Will the answer be correct if you just apply the power rule? Applying only the Power Rule will reault to h'(x) = 2(4x- 3) that is diferent ing only the Power Rule
Transcribed Image Text:L probioiU, 1j uppreciate the siglncance ol chain rule in finding the derivative of a composite function. Learning Task 1: For the given functions f(x) and 9(x), find (fog)(x) 1. f(x) = x2 and g(x) = x+5 2. f(x) = x +1and g(x) = 4x2 -3 %3D 3. f(x) = x3 and g(x) x-1 4. f(x) = sin xand g(r) = 2x %3D 5. f(x) = x2 +cosx and g(x) = 3x+ 4 Guide Questions: 1. How did you calculate (fo g)(x) ? 2. Is the result of the composition simpler or more complex that the combined functions? Learning Task 2: Expand each function (using the appropriate technique/ formula). Compute the derivative of the expanded function by applying the differ- entiation rules. 1. flx) = (x + 5)2 2. f(x) = (4x2 – 3)2 3. f() = (x2 + 2x + 3)2 4. f(x) = (3x - 2)3 5. f(x) = sin (2x) %3! Derivative of Composite Functions and the Chain Rule Given the problem find the derivative of G) = (4x - 3)a how will you do it? Will the answer be correct if you just apply the power rule? Applying only the Power Rule will reault to h'(x) = 2(4x- 3) that is diferent ing only the Power Rule
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