Gradient of log of norm of a matrix

Question

I am working on an optimization problem where I need the gradient $\nabla f(X)$ of $f(X) = log(||TX-Y||^2)$, where X is a vector. My attempt is $\nabla f(X) = \frac {\nabla ||TX-Y||^2}{||TX-Y||^2} = \frac {2(TX-Y)^TT}{||TX-Y||^2}$. Am I correct ?