Toward the spectral index in slow roll

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?