Find f'(2) given the following

Question

Find f'(2) given the following.

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

g(2) = 3 g'(2) = -2

h(2) = 9 h'(2) = 4

Answer 1

f(x) = g(x)√h(x)

Using the Product Rule and Chain Rule, f'(x) = g'(x)√h(x) + g(x)[(1/2)(h(x))^-1/2h'(x)]

So, f'(2) = g'(2)√h(2) + g(2)[(1/2)(h(2))^-1/2h'(2)] = (-2)√9 + 3[(1/2)(1/√9)(4) = -6 + 2 = -4