Question

I hate these

Y= (Square root of x) - 2
________________________

(square root of x) + 2

Calculate dy/dx

Please help, thank you

Answer 1

y = (√x - 2)/(√x + 2)

by the quotient rule

dy/dx = [ (x^(1/2) + 2)( (1/2)x^(-1/2) - (x^(1/2)- 2)((1/2)x^(-1/2) ] / (√x+2)^2
= (1/2)x^(-1/2) [ x^(1/2 + 2 - x^(1/2) + 2]/(√x+2)^2
= (1/2)(1/√x)(4)/(√x+2)^2
= 2/(√x(√x+2)^2 )