Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (b)/Solution 1

Since we have simplified, we can simply apply the chain rule to it using $u = x^{3} + 2 x^{2} + x - 3$ .

$\begin{aligned} f (u) & = e^{u} & f^{'} (u) & = e^{u} \\ u (x) & x^{3} + 2 x^{2} + x - 3 & u^{'} (x) & = 3 x^{2} + 4 x + 1 . \end{aligned}$

Combining, we get:

$f^{'} (x) = (3 x^{2} + 4 x + 1) \cdot e^{x^{3} + 2 x^{2} + x - 3}$