I'm getting lost in the algebra. Can somebody please help me!
I'm trying to get a derivitive of:
x(x^2-6x+16)/(x-2)^3
I've gotten this far:
(x-2)^3(2x-6)-(x^2-6x+16)3(x-2)/((x-2)^2)^3
This is where I get lost.
no need to get lost, the important thing is to bring the expression to a convenient form:
f(x) = x(x^2-6x+16)/(x-2)^3 = (x^3 - 6x^2 + 16x) / (x-2)^3 =
= (x^3 -6x^2 + 16x)*(x-2)^-3
now as you know d/dx(a(x)*b(x)) = a '(x)*b(x) + a(x)*b '(x)
in the present case a(x) = (x^3 -6x^2 + 16x) , b(x) = (x-2)^-3
f '(x) = (3x^2-12x+16)/(x-2)^3 -3*(x^3 - 6x^2 + 16x)/(x-2)^4