not bad, but why did you subtract?
d/dx (x+8)^(1/2) = (1/2)(x+8)^(-1/2)
your derivative is good, except for that.
Find the derivative.
{sqrt(x+8)}*(x^2+20x)
(x+8)^1/2(2x+20) minus (1/2)(x+8)^-1/2(x^2+20x)
I'm not feeling confident I am on the right track and I have a quiz tomorrow over this.
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