Simpllify and Differentiate

[dave turbo]

I am trying to simplify and take the deritive of this -

f(x) = (4x-2x^2+6)/(2x)

f'(x) = (-4x + 4)/(x^2)

f'(x) = (-x^2 +2)/x

is that correct?

 

[HallsofIvy]

I am trying to simplify and take the deritive of this -

f(x) = (4x-2x^2+6)/(2x)

f'(x) = (-4x + 4)/(x^2)

f'(x) = (-x^2 +2)/x

is that correct?

No, that is not correct. "-4x+ 4" is the derivative of the numerator but that alone would not be the numerator and certainly the denominator would not be "x^2".

Since you say simplify and take the derivative, I would be inclined to first write
f(x)= 2- x+ 3/x= 2- x+ 3x^{-1}.

 

[Quaid]

f(x) = (4x-2x^2+6)/(2x)

f'(x) = (-4x + 4)/(x^2)

Were you told to use the Quotient Rule? If so, you could factor 2 from the numerator first, to cancel the 2 in the denominator.

Otherwise, I would divide the numerator by 2x, as HallsofIvy showed; then use the Power Rule to differentiate.

Cheers