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Q8. We shall formally show that if two functions f and q are both differentiable at c, then we have (fg)(c) = f(c)g(c) + f(c)g'(c). f(c+h)g(c+h) - f(c)g(c+h) (a) Show that f"(c)g(c) = lim h-0 f(c)g(c+h)- f(c)g(c) (b) Show that f(c)g'(c) lim h 0 (c) Combine (a) and (b) to show the result.

Q8. We shall formally show that if two functions f and q are both differentiable at c, then we have (fg)(c) = f(c)g(c) + f(c)g'(c). f(c+h)g(c+h) - f(c)g(c+h) (a) Show that f"(c)g(c) = lim h-0 f(c)g(c+h)- f(c)g(c) (b) Show that f(c)g'(c) lim h 0 (c) Combine (a) and (b) to show the result.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
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Q8. We shall formally show that if two functions f and q are both differentiable at c, then we have (fg)(c) = f(c)g(c) + f(c)g'(c). f(c+h)g(c+h) - f(c)g(c+h) (a) Show that f'(c)g(c) = lim h-0 f(c)g(c+h)- f(c)g(c) (b) Show that f(c)g'(c) lim h 0 h (c) Combine (a) and (b) to show the result.
Transcribed Image Text:Q8. We shall formally show that if two functions f and q are both differentiable at c, then we have (fg)(c) = f(c)g(c) + f(c)g'(c). f(c+h)g(c+h) - f(c)g(c+h) (a) Show that f'(c)g(c) = lim h-0 f(c)g(c+h)- f(c)g(c) (b) Show that f(c)g'(c) lim h 0 h (c) Combine (a) and (b) to show the result.
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