Derivative of Composite Function/Examples/Root of x^2 + x + 1

Example of Derivative of Composite Function

 * $\map {\dfrac \d {\d x} } {\sqrt {x^2 + x + 1} } = \dfrac {2 x + 1} {2 \sqrt {x^2 + x + 1} }$

Proof
Let $u = x^2 + x + 1$.

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

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

and so: