Extending Differentiation

Question

Given that y=1/2x-1 + 1/(2x-1)^2, find the exact value of dy/dx when x=2

Answer 1

I reckon that the quantity in the first term ought to have its denominator parenthesized, too, as you did in the second term where the denominator is squared.

 

y' = D_x [(2x-1)^-1 + (2x-1)^-2[ = (-1)(2x-1)^-2(2) + (-2)(2x-1)^-3(2)] and I see no need to simplify this because all you need, to answer this question, is to substitute x=2 and evaluate carefully.