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If h(x) = f(x)g(x), we know h' = f'g+fg. Take another derivative and show that h" = f"g+2f'g' + fg". (Show means, do the computation and then notice that h" is indeed what it is supposed to be.) Show your work. Find a similar formula for h". Show your work.

If h(x) = f(x)g(x), we know h' = f'g+fg. Take another derivative and show that h" = f"g+2f'g' + fg". (Show means, do the computation and then notice that h" is indeed what it is supposed to be.) Show your work. Find a similar formula for h". Show your work.

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
Section3.5: Graphical Differentiation
Problem 1E
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(a) If h(x) = f(x)g(x), we know h' = f'g+fg'. Take another derivative and show that h" = f"g+2f'g' + fg". (Show means, do the computation and then notice that h" is indeed what it is supposed to be.) Show your work. (b) Find a similar formula for h"". Show your work.
Transcribed Image Text:(a) If h(x) = f(x)g(x), we know h' = f'g+fg'. Take another derivative and show that h" = f"g+2f'g' + fg". (Show means, do the computation and then notice that h" is indeed what it is supposed to be.) Show your work. (b) Find a similar formula for h"". Show your work.
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