# Calculus III Derivative

Given that X is a vector in R^n, what is the derivative of:

$$\texts{f(X)=|X|^{2}X}$$

I basically combined the product formula and dot product rule after breaking down |X|^2, which yielded my answer of:

$$\texts{f'(X)=|X|^{2}v+2(v\bullet X)X}$$

Where v the direction.

Is this correct/ close?