# Find Adjoint of Product & Sum of Differential Operator

I am asked to find the adjoint of the following differential operators:

$$$$L_{1} = a(x)\frac{\partial}{\partial x}b(x)\frac{\partial}{\partial x},$$$$

and

$$$$L_{2} = \frac{\partial}{\partial t} + b(x)\frac{\partial}{\partial x},$$$$

From my understanding

$$$$adj(\frac{\partial}{\partial t}) = -\frac{\partial}{\partial t}$$$$

and

$$$$adj(\frac{\partial^2}{\partial t^2}) = \frac{\partial^2}{\partial t^2}$$$$

Can somebody please explain how to find the adjoint of the two operators? Thank you!