Can anyone please tell me how to calculate discrete wavelet transform of a derivatve?

Question

if $W^{m}[]$ is the wavelet transform of any function at decomposition level m, then how can I calculate

$W^{m}[\frac{d}{dx} f(x)]$,

if fact I want to know if

$W^{m}[\frac{d}{dx} f(x)] = \frac{d}{dx}(W^{m}[f(x)])$ and if this does not hold, why?