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 $u=x^{3}+2x^{2}+x-3$.

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

Combining, we get:

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