dada a função f(x) = log (x² - 4x +4)², determine: 1. f`(4) 2.f`(10)

Função f(x):

-> f(x) = log[ (x^2 - 4x + 4)^2 ]

-> f(x) = log[ (x - 2)^2 ]^2

-> f(x) = log[ (x - 2)^4 ]

-> f(x) = 4log(x - 2)

Portanto, a derivada f'(x) é:

-> f'(x) = 4[ log(x - 2) ]'

-> f'(x) = 4[ log(e)/(x - 2)* (x - 2)' ]

-> f'(x) = 4[ log(e)/(x - 2)* 1 ]

-> f'(x) = 4 log(e)/(x - 2)

1. f'(4):

-> f'(x) = 4 log(e)/(x - 2)

-> f'(4) = 4 log(e)/(4 - 2)

-> f'(4) = 4 log(e)/2

-> f'(4) = 2 log(e)

1. f'(10):

-> f'(x) = 4 log(e)/(x - 2)

-> f'(4) = 4 log(e)/(10 - 2)

-> f'(4) = 4 log(e)/8

-> f'(4) = log(e)/2

Se gostou, dá um joinha!