How to prove Bernoulli distribution belongs to the exponential family

According to a book, a distribution belongs to the exponential family if it can be written in the form of

I wrote the Bernoulli distribution as $\exp\Big(y \log\,[{\mu}/{(1-\mu)}] + \log\,(1-\mu)\Big)$. In this case $a(y)=y$, $b(\theta)= \log\,[{\mu}/{(1-\mu)}], c(\theta)=\log(1-\mu)$, but don't know what $d(y)$ is. Any idea what it is and why?

• If you have the entire pdf without using $d$, then won't it be the case that you just have $d(y)=0$? – Glen_b Nov 27 '14 at 23:39

$${}{}{}{}{}d(y)=0{}{}{}{}{}$$
• That is what I thought, but since this is the first case I have come across in which $d(y)=0$, I wasn't sure. – Günal Nov 28 '14 at 12:55