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6. Find h' (÷) , h" (), and h" (G), given h(r) = sin r cos 3r.

6. Find h' (÷) , h" (), and h" (G), given h(r) = sin r cos 3r.

Calculus: Early Transcendentals
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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6. Find M (),M" (중), and h" G), given h(r) = sin r cos 3r. 7. If f(r) = 625 – 5x* + 3r3 – 722 + 9x – 14, then find f(n)(x) for all r E N. For problems (8) and (9), please refer to the table below: f(1) | g(x) | f'(1)| g'(r) 1 (fog)(x) | (f ° g)(r) -1 -1 2 -2 1 2 -1 1 -2 -1 2 1 1 -1 8. Use the table of values to determine (ƒ o g)(r) and (f o g)'(r) at r =1 and r = 2. 9. Use the table of values to determine (ƒ o g)(x) and (f o g)'(r) at r = -2, –1 and 0. 10. Show that 2"+42' + 8z = 0 if z = e-2#(sin 2r + cos 2r). 11. If f(r) = r' and g(r) = r², then f'(r) = 4r³ and gʻ(r) = 3r². The Chain Rule multiplies derivatives to get 12r. But ƒ (g(x)) = (r³)* = r²² and its derivative is NOT 12r. Where is the flaw? %3D 2.
Transcribed Image Text:6. Find M (),M" (중), and h" G), given h(r) = sin r cos 3r. 7. If f(r) = 625 – 5x* + 3r3 – 722 + 9x – 14, then find f(n)(x) for all r E N. For problems (8) and (9), please refer to the table below: f(1) | g(x) | f'(1)| g'(r) 1 (fog)(x) | (f ° g)(r) -1 -1 2 -2 1 2 -1 1 -2 -1 2 1 1 -1 8. Use the table of values to determine (ƒ o g)(r) and (f o g)'(r) at r =1 and r = 2. 9. Use the table of values to determine (ƒ o g)(x) and (f o g)'(r) at r = -2, –1 and 0. 10. Show that 2"+42' + 8z = 0 if z = e-2#(sin 2r + cos 2r). 11. If f(r) = r' and g(r) = r², then f'(r) = 4r³ and gʻ(r) = 3r². The Chain Rule multiplies derivatives to get 12r. But ƒ (g(x)) = (r³)* = r²² and its derivative is NOT 12r. Where is the flaw? %3D 2.
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