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

Example of Derivative of Composite Function

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

Proof
Let $u = 1 + x$.

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

Thus by definition of square root we have:
 * $y = \paren {1 + x}^{1/2}$

and so: