Notation for weak solutions in space and time

Question

If we have a function $f\in L^q(0,T,W^{1,q}(\mathbb{R}^n))$, does this notation also mean that the partial derivative of $f$, that is $\partial_t f$, is in $L^q$? Or, for this to hold, would it need to be $f\in W^{1,q}(0,T,W^{1,q}(\mathbb{R}^n))$? I know that I just recently asked about this notation but it's still not completely clear to me and I don't know anybody I could ask for help in person. Thanks in advance!