partial derivative of $L^2$ norm?

In the chapter on energy methods for partial differential equations I saw the following: $$\frac{d\|u\|_2^2}{dt}=(u,u_t)+(u_t,u)=\cdots$$ So, why we can't just write $$\frac{d\|u\|_2^2}{dt}=2(u,u_t)=\cdots?$$

Are these two the same, or there is a reason I have to consider the derivative as in the first expression?