The Duchess of Cambridge has carried out her first official engagement since announcing that she is expecting her third child.To mark World Mental Health day, Kate joined Prince William and Prince Harry at a Buckingham Palace reception to celebrate the contribution of those working in the mental health sector across the UK. The Duchess, who is in the early stages of her pregnancy, wore a blue lace gown with a black bow at the neckline for the occasion which showed off the slightest sign of her baby bump.When news of Kate's pregnancy broke on 4 September, Kensington Palace confirmed she was suffering from Hyperpremesis Gravidarum, a rare form of morning sickness. This has forced her to miss a a number of recent engagements, including Prince George's first day at school. However, William revealed his wife had been 'feeling better' when chatting to guests at an awards ceremony in London two weeks ago.Kate looked to have made a full recovery as she arrived at the event on Tuesday evening, where she met guests invited from leading mental health organisations. Earlier in the day, the Duke and Prince Harry hosted a reception at St James's Palace to celebrate the impact of their Heads Together campaign, which aims to get the country talking about mental health.