derivative of ((5x-4) / sqrt (5x^2 - 8x + 4))

Question

How do I get the final answer?

Answer 1

Quotient rule:

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

f ' (x) = (g'(x) * h(x) - h'(x) * g(x)) / (h(x))^2

g(x) = 5x - 4

g'(x) = 5

h(x) = (5x^2 - 8x + 4)^(1/2)

h'(x) = (1/2)(5x^2 - 8x + 4)^(-1/2)(10x - 8)

h'(x) = (5x - 4)(5x^2 - 8x + 4)^(-1/2)

f ' (x) = ( 5(5x^2 - 8x + 4)^(1/2) - (5x - 4)(5x - 4)(5x^2 - 8x + 4)^(-1/2) ) / (5x^2 - 8x + 4)

f ' (x) = ( 5(5x^2 - 8x + 4)(5x^2 - 8x + 4)^(-1/2) - ((5x - 4)^2)(5x^2 - 8x + 4)^(-1/2) ) / (5x^2 - 8x + 4)

f ' (x) = ( 25x^2 - 40x + 20 - 25x^2 + 40x - 16)(5x^2 - 8x + 4)^(-1/2) / (5x^2 - 8x + 4)

f ' (x) = 4 / (5x^2 - 8x + 4)^(3/2)