Differentiating a cubed root? True/false: As a fraction, the cube root of 63 is about 191/48 (differentials question).
Am I supposed to solve this by differentiating $63^{1/3}$? So, 63 times 1/3$^{-2/3}$? So, it's false? 

I imagine you are meant to notice that $64=4^3$ and hence to say that the cube root is $4\left(1-\frac{1}{64}\right)^{1/3}$. You take $(1-x)^{1/3}=1-\frac{x}{3}+O(x^2)$, so the root is about $4-\frac{1}{48}=\frac{191}{48}$
