Question

Step by Step solution please.
Thanks

Answer 1

Derivation of f(x):

`f'(x) = (g(x)*8x-4x^2*g'(x))/((g(x))^2) -(1)/(x+2)`

Since g(3) = 6 and g'(3) = 3

`f'(3) = (g(3)*8*3-4(3)^2*g'(3))/((g(3))^2) -(1)/(3+2) \\f'(3) = (6*8*3-4*9*3)/(36) -(1)/(5) \\f'(3) = (36)/(36) -(1)/(5) =1-(1)/(5) =(4)/(5)\\ f'(3) = 0.8`

Thus f'(3) = 0.8

Hope that helps!

A couple of identities I used in derivation:

`(d)/(dx) (ln x) = (1)/(x)`