Final answer:
To find a differential operator that annihilates a given function, we need to find an operator that, when applied to the function, yields zero. For example, if the given function is f(x) = sin(x), the differential operator that annihilates it is d/dx, which represents the derivative with respect to x.
Step-by-step explanation:
In mathematics, differential operators are used to express the rate of change of a function. To find a differential operator that annihilates a given function, we need to find an operator that when applied to the function, yields zero.
For example, if the given function is f(x) = sin(x), the differential operator that annihilates it is d/dx, which represents the derivative with respect to x. When we apply this operator to the function, we get d/dx (sin(x)) = cos(x), which equals zero.
Thus, the differential operator d/dx annihilates the function sin(x).