
Brice W.
asked 01/24/25The functions f(x) and g(x) are differentiable. The function h(x) is defined as: h(x)=f(x)+g(x) If f(6)=9, f′(6)= – 4, g(6)= – 6, and g′(6)= – 3, what is h′(6)? Simplify any fractions. h′(6)=
3 Answers By Expert Tutors

Mira P. answered 01/25/25
Hi! I am Mira; a college student looking to help tutor!
Since h(x) = f(x)+g(x) and we need to find h'(6), step one is to find h'(x).
h'(x)=f'(x) + g'(x).
That means that h'(6) will equal f'(6)+g'(6)
h'(6)= -4+-3, which is -7.
Therefore, h'(6) will equal -7.
h(x)=f(x) + g(x)
h'(x)= f'(x) +g'(x)
h'(6)= f'(6)+g'(6)
h'(6)= -4-3
= -7
Hope that helps !!
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Doug C.
This problem would be much more interesting (using all the given info), if h(x) = f(x)g(x), i.e. product of the two given functions. h'(x) = f(x)g'(x)+g(x)f'(x) -- using the product rule. Wonder if that is what was intended?01/28/25