How can I simplify this derivative?

[DespicableMe]

Homework Statement

h(x) = (x² + 3) / (2x - 1)
And if f = the numerator
And if g = the denominator,

h'(x) = (f/g)'
= [ (x²)' + 3' ) * (2x - 1) ] - [ ((2x)' - 1')) * (x² + 3) ] ALL DIVIDED BY (2x - 1)²

= [2x (2x - 1) - 2 (x² + 3) ] ALL DIVIDED BY (2x - 1)²


Would I then use the chain rule for the denominator?

 

[Pengwuino]

Why would you use the chain rule? That's the answer.

 

[DespicableMe]

Why would you use the chain rule? That's the answer.

Oh, because I thought the denominator resembled a function in a function, so I thought I could use the chain rule.
But if I did, that would be like taking the derivative of the derivative, right?

 

[Pengwuino]

Sorry, I didn't see something you wrote. That's not how the quotient rule works. You don't simply take separate derivatives for the numerator and denominator. You do exactly what you already did, which was

$$h'(x) = {{g(x)f'(x) - f(x)g'(x)} \over g(x)^2}$$

That's it.

 

[DespicableMe]

Sorry, I didn't see something you wrote. That's not how the quotient rule works. You don't simply take separate derivatives for the numerator and denominator. You do exactly what you already did, which was

$$h'(x) = {{g(x)f'(x) - f(x)g'(x)} \over g(x)^2}$$

That's it.

Thanks, that makes a lot more sense.