Question 202798
I was working on this problem when I noticed that Stanbon got to it first, but after looking at his solution, I don't quite understand how he arrived at what he got!  So here's my take on it.
Find the derivative of:
{{{f(x) = x^4*e^(3x)}}}
Since you are asked to find the derivative of a product of two functions of x, you will need to use the following rules of differential calculus:
{{{d(u*v)/dx = u*(dv/dx) + v*(du/dx)}}} also:
{{{d(e^m)/dx = e^m*(dm/dx)}}} Note: u, v, and m are all functions of x.
So here we go: 
{{{d(f(x))/x = x^4*(d(e^(3x))/dx) + e^(3x)*(d(x^4)/dx)}}}
{{{d(f(x))/dx = x^4*e^(3x)*3 + e^(3x)*4x^3}}} Factor out {{{e^(3x)}}}
{{{highlight(d(f(x)) = e^(3x)(3x^4+4x^3))}}}