What is the derivative of a vector function in Calculus III?

[rman144]

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?

 

[Dick]

Yes, it is. If you mean v(t)=X'(t) and X(t) is a curve.