Question

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

Answer 1

The constant factor remains a multiplier.

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 ...

`(d)/(dx)\left(-(5)/(2x)\right)=\left(-(5)/(2)\right)\left((-1)/(x^2)\right)=(5)/(2x^2)`