Problem: Given that F (w) = cos(sin w) find F'(). Round your answer to 3 decimal places.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A student hands in the following work:
Problem: Given that F (w) = cos(sin w) find F' () . Round your answer to 3
decimal places.
Student answer:
Line 1: The variable here is w , but the method used to differentiate is the same as if the
variable had been x .
Line 2: Recall that the derivative of y= cos x is y = – sin x and the derivative of
y = sin x is y'
= COs x.
Line 3: Using the Product Rule, we get:
Line 4: F' (w) =
sin(sin w) + cos(cos w)
Line 5: To find F' (4)
we need to evaluate F' (uw) at w =
Line 6: F' (4) = - sin(sin ) + cos (cos )
Line 7: F' () = – sin
+ cos
+(수)
Line 8: Using a calculator to evaluate this, we get:
Line 9: F' () -0.6496369391 + 0.7602445971
Line 10: F' (") -0.650 +0.760 = 0.l10
Line 11: So the final answer (to 3 decimal places) is 0.110
Transcribed Image Text:A student hands in the following work: Problem: Given that F (w) = cos(sin w) find F' () . Round your answer to 3 decimal places. Student answer: Line 1: The variable here is w , but the method used to differentiate is the same as if the variable had been x . Line 2: Recall that the derivative of y= cos x is y = – sin x and the derivative of y = sin x is y' = COs x. Line 3: Using the Product Rule, we get: Line 4: F' (w) = sin(sin w) + cos(cos w) Line 5: To find F' (4) we need to evaluate F' (uw) at w = Line 6: F' (4) = - sin(sin ) + cos (cos ) Line 7: F' () = – sin + cos +(수) Line 8: Using a calculator to evaluate this, we get: Line 9: F' () -0.6496369391 + 0.7602445971 Line 10: F' (") -0.650 +0.760 = 0.l10 Line 11: So the final answer (to 3 decimal places) is 0.110
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