y = sqrt(2x+1)(x^3)
I always screw this up, so if someone could just walk through the steps so I could compare, I'd really appreciate it.
Thanks.
You can leave it, but technically you have a radical in the denominator:
$\displaystyle \frac{dy}{dx} = x^{3} \frac{1}{2\sqrt{2x + 1}} + 3x^{2} \sqrt{2x+1} $
So
$\displaystyle \frac{dy}{dx} = \frac{x^3 \sqrt{2x + 1}}{4x + 2} + 3x^{2} \sqrt{2x+1} $
It really depends on how you are going to use the derivative from here on.
-Dan