Question

how to d/dx x^2/(x-1)^(1/2)? [ans: (x(3x-4))/(2(x-1)^(3/2))but i get (x(3x-4))/(2(x-1)^(5/2))].

Answer 1

change it to x^2 * (x-1)^-.5

d/dx= 2x*(x-1)^-.5 + x^2 * (-.5)*(x-1)^-1.5

now, common denominator of (x-1)^1.5

2x(x-1) -.5 x^2 all over denominator

2x^2-2x -.5 x^2=3/2 x^2-2x= (3x^2-4)/2 over denominator

I agree with book answer.