Suppose you are given functions f(x) and g(x), for which f(0)=4, g(x)=6, f prime(0)=-4, and gprime(0)= 5?

find h prime(0) for the function h(x)=g(x)f(x)

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A few days ago

Anonymous

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I take it that by fprime you mean f’ or the derivative of f, and similarly for g and h. I am assuming also that g(x) = 6 should say g(0) = 6.

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

h'(0)= g'(0)f(0) + g(0)f'(0)

= 5*4 + 6*(-4)

= 20 – 24

= -4.

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