Let h(x)=f(x)g(x). If f(x)=x2+10, g(3)=5, and g′(3)=10. Find h′(3).

Answer 1

h(x) = f(x) g(x)

f(x) = x² + 10

g(3) = 5

g'(3) = 10

f'(x) = 2x

∴ f(3) = 19 & f'(3) = 6

d/dx( h(x) ) = d/dx( f(x) g(x) )

Applying Product Rule ( (uv)' = u v' + u' v ) to the right-hand side of the equation:

h'(x) = f(x) g'(x) + f'(x) g(x)

h'(3) = (19)(10) + (6)(5) = 190 + 30

∴ h'(3) = 220

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