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

Example of Derivative of Composite Function

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

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

Let $y = e^u$.

Thus we have:
 * $y = e^{x^2 + x + 1}$

and so: