While trying to find the tangent line to
$y=(1+x^\frac{2}{3})^\frac{3}{2}$
at $x=-1$, I determined the derivative,
$\frac{dy}{dx}=\frac{\sqrt{x^\frac{2}{3}+1}}{\sqrt[3]{x}},$
to get the slope of the tangent. Now that doesn't really help much, since $\sqrt{(-1)^{2/3}+1} = 0$.
I know the result is supposed to be $y=2^{3/2}-\sqrt{2}(x+1)$, though I have no idea why.
Thanks for your help!