# Derivative of Composite Function/Examples/(3x+1)^2

## Example of Derivative of Composite Function

$\map {\dfrac \d {\d x} } {\paren {3 x + 1}^2} = 6 \paren {3 x + 1}$

## Proof

Let $u = 3 x + 1$.

Let $y = u^2$.

Then we have:

$y = \paren {3 x + 1}^2$

and so:

 $\ds \dfrac {\d y} {\d x}$ $=$ $\ds \dfrac {\d y} {\d u} \dfrac {\d u} {\d x}$ Derivative of Composite Function $\ds$ $=$ $\ds 2 u \cdot 3$ Derivative of Square Function, Derivative of Identity Function: Corollary $\ds$ $=$ $\ds 6 \paren {3 x + 1}$ simplification

$\blacksquare$