How to derive det(I + A) ≈ 1 + Tr(A) for infinitesimal A

[spookyfish]

Hi. I am reading a physics text, and in one of the lines it uses the following relation:
$$\mathrm{det}(\delta^\mu_\lambda +\frac{\partial \delta x^\mu}{\partial x^\lambda}) = 1 + \mathrm{Tr}\frac{\partial \delta x^\mu}{\partial x^\lambda}$$
where $\mu$ and $\lambda$ are matrix elements, and $\delta^\mu_\lambda$ is Kronecker's delta. I am trying to derive this, but I am not sure how. Help will be appreciated

 

[micromass]

It looks more like an approximation than an identity. I think they use this: http://en.wikipedia.org/wiki/Determinant#Derivative

 

[spookyfish]

Hi. You are right... Thank you!