First, the AD curve implies the price level and Real GDP is negatively related,i.e Price increase, GDP decrease vice versa.
Reason of downward sloping AD curve.
1,Interest Rate effect.When price level increase, money demand also increase( household need more money to pay for their daily living cost) giving constant money supply, the interest rate has to be  increased to make the money market equilibrium.Increase Rate increase, investment decrease, so the gdp decrease. Implying a downward sloping AD curve
Conclusion: Assume money supply constant.
Price increase---> Money Demand increase-----> Interest Rate increase------> Investment Decrease-----> AD decrease

不是用IS-LM推导出来的么

AD曲线函数为Y=Y(M/P,G,T)，M/P代表真实货币量，真实货币量高时，人们需求就会更高，这是好理解的。那么Y与M/P就成正比，当名义货币量M，ZF支出G与税收T不变时，Y与P自然成反比，表现在坐标轴中即为向下倾斜的曲线