Calculus Question

Question

Use the given information to find f '(9)

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

g(9) = 8 and g'(9) = 9

h(9) = 4 and h'(9) = -6

f'(9) =

Answer 1

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This one is going to be an application of the Power Rule ...

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

which means that

f ‘ (x) = g(x) * h’(x)  + h(x) * g ‘(x)

plugging in the values given at x = 9 that becomes

f ‘ (9) = g(9) * h’(9) + h(9) * g ‘ (9)

=8(-6) + 4(9)

= -48 + 36

= -12

The end value here would be f ‘ (9) = -12