Because it is talking about the derivative, this is the "difference quotient", .
Because f, here, is defined by different formulas for x< 0 and x> 0, you must use the limits "from the right" and "from the left".
As h approaches 0 "from the left, 0+ h= h< 0 so . f(0)= sin(3(0))= 0 so, for h< 0, .
As h approaches 0 "from the right", 0+ h= h> 0 so . for h> 0, .
To find that limit, you will need to remember a limit formula for and use the fact that .
The function, f, will be differentiable at x= 0 if and only if those two one sided limits are the same.