Question

Find the derivative f(x)= 2x / sqrt[x^(2) -1]

Answer 1

use the quotient rule u = 2x v = (x^2-1)^-1/2

du/dx = 2 dv/dx = -1/2 (x^2 -1)^-3/2 2x

\[dy/dx = {(v \times du/dx - u \times dv/dx)}/{v^2} \]

\[(x^2 -1)^{-1/2} \times 2 - 2x \times -x(x^2 -1)^{-3/2})/((x^2-1)^{-1/2})^2 \]

you can simplify the derivative