# Setting Derivative = 0 and solving

1. Oct 17, 2013

### deedsy

1. The problem statement, all variables and given/known data
I'm currently working on a problem that requires me to set the derivative = 0 and solve for a variable (call it x). The derivative comes out to be a fraction, with x terms in both the numerator and denominator. Is it legal to just multiply 0 by the denominator (thereby canceling it) even if it has the term of interest as part of it?

Simple Ex: say the derivative came out to be x-3 / 2x. And I want to solve for x.
When I set that derivative equal to zero, can i just multiply 0 by 2x, leaving x-3=0? So x=3

2. Relevant equations

none

3. The attempt at a solution
...

2. Oct 17, 2013

### rcgldr

That should be ok. You could also divide the left side by x / x, assuming that x is not equal to zero, resulting in:

( 1 - (3/x) ) / 2 = 0

3. Oct 17, 2013

### deedsy

thank you

4. Oct 17, 2013

### MGCLO

i thought they're supposed to show the work?

5. Oct 17, 2013

### deedsy

It is a requirement for HW problems, but my question was geared towards a concept. The equation I'm deriving for the HW would probably take up an entire line on here. The example I put on was just that, an example, it wasn't even close to my actual problem (although I wish it was haha)

6. Oct 17, 2013

### rcgldr

Multiplying both sides by 2x is just as valid as dividing the left side by x/x. I only showed that as an alternative in case there's a situation where that would be a better option for a different equation.