Help with derivatives?

Question

(sqrt(20x^2 + 5)) / (5x^2)

How do you solve this, i know you use quotient rule, and chain rule, but when i get to (20x^2 + 5)^1/2 x (5x^2)

Please help.

Answer 1

u = (20x^2)^1/2 v= 5x^2
du = (1/2)(20x^2 + 5)^(-1/2) dx dv=10x

[(10x)(20x^2 +5)^(1/2)] - [((5x^2)/2)(20x^2 +5)^(1/2)]
and divide whole thing by 5x^4

when you simpify it'll be
(2/x)(20x^2+5)^(1/2) - (1/2)(20x^2+5)^(1/2)

Answer 2

[(5x^2)(40x)(1/2)(20x^2+5)^-(1/2) - (sqrt(20x^2 + 5))(10x)]/(25x^4)
=[100x^3/(sqrt(20x^2 +5)) -(sqrt(20x^2+5))(10x)]/(25x^4)

You can simplify it more, but I'll let you do it. Sweetchi forgot to square the 5.