Question

Calculus question?

I need help simplifying this function. This is regarding the quotient rule.

Thank you!

Answer 1

Remark
If you don't start exactly the right way, you can get into all kinds of trouble. This is just one of those cases. I think the best way to start is to divide both terms by x^(1/2)

Step One
Divide both terms in the numerator by x^(1/2)
y= 6x^(1/2) + 3x^(5/2 - 1/2)
y =6x^(1/2) + 3x^(4/2)
y = 6x^(1/2) + 3x^2 Now differentiate that. It should be much easier.

Step Two
Differentiate the y in the last step.
y' = 6(1/2) x^(- 1/2) + 3*2 x^(2 - 1)
y' = 3x^(-1/2) + 6x I wonder if there's anything else you can do to this. If there is, I don't see it.

I suppose this is possible.
y' = 3/x^(1/2) + 6x

y' =
`(3 + 6x^(3/2))/(x^(1/2))`

Frankly I like the first answer better, but you have a choice of both.