# Thread: Chain Rule or Product Rule ?

1. ## Chain Rule or Product Rule ?

This is the expression:

C(x)=x(3x-(500+6x))

My questions are:

1. Am I am supposed to use the chain rule because there is a function within a function ? If so, what happens to the x outside ? Or better question: which terms/functions would be considered outside functions and which is considered an inside function ?
2. Or am I supposed to use the product rule because the x is outside of the rest of the function ? (Not feeling confident about this option)
I am totally confused and to top it off the Chain Rule really confuses me. I can figure it out if I see an example worked out but I haven't been able to find examples that look exactly like this which makes me think I am trying to use the wrong rule.

2. Hello,

If you develop the thing, product rule will be enough

If you apply chain rule, you can, but it's quite complicated as there are several functions into others...

3. ## Develop ?

Originally Posted by Moo
Hello,

If you develop the thing, product rule will be enough

If you apply chain rule, you can, but it's quite complicated as there are several functions into others...

By develop do you mean:

3x^2-(500x+6x^2) ?

If so...

Still confused

4. Don't use the chain rule, because you really don't have composite functions (Use Chain Rule more for Trig or Log or Exponentials of other functions)

You could use the product rule here, but since these are pretty simple terms, the easiest thing to do is just to multiply it all out, simplify it, then take the derivative.

$\displaystyle C(x)=x(3x-(500+6x))$
$\displaystyle C(x)=x(3x-500-6x)$
$\displaystyle C(x)=x(500-3x)$
$\displaystyle C(x)=500x-3x^2$
$\displaystyle C'(x)=500-6x$