the function is x/(square root(x-1)) . find the derivative with respect to x

so i have this so far;

((x-1)^(1/2) - (X)(1/2)(x-1)^(-1/2))/(x-1)^(3/2)

im stuck for the next steps

Printable View

- Mar 19th 2011, 07:48 AMnando29finishing a quotient rule problem
the function is x/(square root(x-1)) . find the derivative with respect to x

so i have this so far;

((x-1)^(1/2) - (X)(1/2)(x-1)^(-1/2))/(x-1)^(3/2)

im stuck for the next steps - Mar 19th 2011, 08:01 AMicemanfan
Hi Nando, your first step is not quite correct. The denominator should just be $\displaystyle x - 1$, not $\displaystyle (x - 1)^{3/2}$. You might want to consider writing the original function as $\displaystyle \frac{x}{\sqrt{x - 1}} = \frac{x - 1 + 1}{\sqrt{x - 1}} = \frac{x - 1}{\sqrt{x - 1}} + \frac{1}{\sqrt{x - 1}} = \sqrt{x - 1} + \frac{1}{\sqrt{x - 1}}$. This way you can take the derivative easily without having to use the quotient rule.