Question

Differentiate each function
34. [(x^2 + x)/(x^2 - x)]^1/2

My answer:
[(-2x^2)]/[(x^2 + x)^1/2 * (x^2-x)^3/2]

The book's answer is:
[(-1)] / [(x-1)^3/2 * (x + 1)^1/2]

Answer 1

I am going to simplify the function first, but that will not affect the correct answer. It is easier to differentialte if it has fewer terms.
f(x)= [(x^2 + x)/(x^2 - x)]^1/2
= [x(x+1)/x(x-1)]^1/2
= [(x+1)/(x-1)]^1/2
Derivative:
df/dx = (1/2)[(x+1)/(x-1)]^-1/2*
[(x-1)-(x+1)]/(x-1)^2
=[-(x-1)/(x+1)]^1/2*
[(x-1)^2]
= -(x-1)^-3/2 * (x+1)^-1/2