Math Problem Statement
Use the information about values of the functions and their derivatives to calculate 𝐻′(7),H′(7), where 𝐻(𝑥)=𝑥𝑔(𝑥)𝑓(𝑥).H(x)=xg(x)f(x).
𝑓(7)f(7)
𝑓′(7)f′(7)
𝑔(7)g(7)
𝑔′(7)g′(7)
33
−5−5
77
−4−4
(Give an exact answer. Use symbolic notation and fractions where needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Product Rule
Differentiation
Formulas
H'(x) = g(x) f(x) + x * (g'(x) f(x) + g(x) f'(x))
Product Rule: (uv)' = u'v + uv'
Theorems
Product Rule
Suitable Grade Level
Grades 11-12