Derivative of Composite Function/Examples/Root of x + 1 over x - 1

Example of Derivative of Composite Function

 * $\map {\dfrac \d {\d x} } {\sqrt {\dfrac {x + 1} {x - 1} } } = -\dfrac 1 {\sqrt {\paren {x + 1} \paren {x - 1}^3} }$

Proof
Let $u = \dfrac {x + 1} {x - 1}$.

Let $y = u^{1/2}$.

Thus we have:
 * $y = \paren {\dfrac {x + 1} {x - 1} }^{1/2}$

and so: