Question
Asked Sep 29, 2019
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Use the information about values of the functions and their derivatives to calculate H′(9), where H(x)=x/g(x)f(x)

f(9)=7 ; f'(9)=-2 ; g(9)=4 ; g'(9)=-4

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Expert Answer

Step 1

Use quotient rule first. 

X
Н()-
g(x)f (х)
Н()- Х)8(х)f (х)-x[g(x)f(х)]"
[g(x)г(х)]?
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X Н()- g(x)f (х) Н()- Х)8(х)f (х)-x[g(x)f(х)]" [g(x)г(х)]?

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Step 2

Then apply product rule for [g...

H'(x)Xg(x)f (x)-x[g(x)f(x)]"
g(x)f(x)]2
H'(x)=g(x)f(x)-x[g'(x)f(x)+g(x)f'(x)]
g(x)f(x)]2
H'x)=g(x)f(x)-x[g'(x)f(x)+g(x)f'(x)]
g(x)f(x)]2
help_outline

Image Transcriptionclose

H'(x)Xg(x)f (x)-x[g(x)f(x)]" g(x)f(x)]2 H'(x)=g(x)f(x)-x[g'(x)f(x)+g(x)f'(x)] g(x)f(x)]2 H'x)=g(x)f(x)-x[g'(x)f(x)+g(x)f'(x)] g(x)f(x)]2

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