How to calculate $f'(t)$, where $f:I\to\mathbb{R}^{n^2}$ is given by $f(t)=X(t)^k$?

How to calculate $f'(t)$, where $f:I\to\mathbb{R}^{n^2}$ is given by
$f(t)=X(t)^k$?

Let $I$ be a interval, $\mathbb{R}^{n^2}$ be the set of all $n\times n$
matrices and $X:I \to\mathbb{R}^{n^2}$ be a differentiable function. Given
$k\in\mathbb{N}$, define $f:I\to\mathbb{R}^{n^2}$ by $f(t)=X(t)^k$. How to
calculate $f'(t)$ for all $t\in I$?
Thanks.