Find the derivative of F(x) = (8x^3 - 1)/(2x - 1), is this right?

[mustang]

Homework Statement

22. Divide the expression before differentiating.

F(x) = (8x^3 - 1)/ (2x - 1)

Homework Equations

F'(x) = An^(x-1)

The Attempt at a Solution

F(x) = [(8x^3) / (2x - 1)] - [(1)/(2x - 1)]
= [(4x^2)/(1)] - [(1) / (2x - 1)]
= (4x^2) - (2x-1)^-1

F'(x) = (8x + 1)

 

[malawi_glenn]

2. Homework Equations
F'(x) = An^(x-1)

?

And this is wrong:
F(x) = [(8x^3) / (2x - 1)] - [(1)/(2x - 1)]
= [(4x^2)/(1)] - [(1) / (2x - 1)]

And even if that was right; the derivative of (4x^2) - (2x-1)^-1
is not (8x + 1)

The general rule for differentiation these kinds of functions are: x^n = n x^(n-1) Then you have rules for inner- and outer derivatives. I suggest you do the division of F(x) again, if you don't remember how to divide polynomials, you should look it up again.

 

[NonAbelian]

try this instead: (regard this as long division, not a square root!)

2x-1 \sqrt{8x^3+0x^2+0x-1}

And remember, whatever you get in the end, your derivative has a discontinuity at x=1/2!