Derivative of Composite Function/Examples/(a x^2 + b x + c)^3

Example of Derivative of Composite Function

 * $\map {\dfrac \d {\d x} } {\paren {a x^2 + b x + c}^3} = 3 \paren {2 a x + b} \paren {a x^2 + b x + c}^2$

Proof
Let $u = a x^2 + b x + c$.

Let $y = u^3$.

Thus we have:
 * $y = \paren {a x^2 + b x + c}^3$

and so: