How would I solve this using derivative rules? I know the answer is 5/2x^2 but what I don’t understand is how you get that. Because with the power rule I thought you had to take the derivative of both separately, and the derivative of 5/2 is 0

  The constant factor remains a multiplier.

Step-by-step explanation:

The derivative of "a·f(x)" is a·f'(x). That is, the constant multiplier remains a constant multiplier, unchanged.

For ax^-1, the derivative is a(-x^-2) per the power rule. For your value of a=-5/2, this is ...

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.