Toward the spectral index in slow roll

[ergospherical]

Getting a bit confused over a manipulation; I have a power spectrum $P_{R}(k)$ in terms of $V$ and $\epsilon_V$ (to be evaluated at $k=aH$) for the curvature perturbation $R$ and from this need to get a spectral index, i.e. apply $d/d(\ln{k})$. So we need to transform this operator into "something" $\times d/d\phi$. From slow roll we get $3H \dot{\phi} = -V'$ and $H^2 = V/(3M_{pl}^2)$, combining to$$\frac{\dot{\phi}}{H} = -\frac{M_{pl}^2 V'}{V}$$Then from the LHS I need to convert into something related to $d\phi/dk$. We know $k=aH$ so could try something like$$\frac{\dot{\phi}}{H} = a \frac{d\phi}{da} = a \frac{d\phi}{dk} \frac{dk}{da}$$but from there on it's not clear to me how to manipulate $\frac{dk}{da}$ into something without more time derivatives? The answer should be$$\frac{d}{d\ln k} = - M_{pl}^2 \frac{V'}{V} \frac{d}{d\phi}$$i.e. suggesting that $$\frac{a}{k} = \frac{da}{dk}$$ but why is that the case, as $H = H(t)$ is not fixed?