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anonymous
 one year ago
Given that h(x)=x^2g(x) and g(3)=5 and g'(3)=7 find h'(3)
anonymous
 one year ago
Given that h(x)=x^2g(x) and g(3)=5 and g'(3)=7 find h'(3)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You can use the product rule. h'(x) = f(x)g'(x) + g(x)f'(x) where in this problem f(x) = x²

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so f(x)=x^2 and f'(x)=2x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then evaluate them both at 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what about g(x) and g'(x)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well they're asking for h'(3), so you don't need g(x) and g'(x) since they gave you the values at 3.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so how would you use the product rule?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Above is the product rule generally. Specifically at x = 3. \[h'(3) = f(3)g'(3) + g(3)f'(3)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0g(3) and g'(3) are given. f(3) and f'(3) are found by evaluating x² and 2x at 3 respectively

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh is it h'(3)=9*7+5*6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(3) = 3² = 9 f'(3) = 2(3) = 6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks for your help peachpi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes that's right. You're welcome
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