Originally Posted by
ecMathGeek That solution is not possible. I went ahead and did some of the work (before noticing that the solution is not possible) so I'll post it anyways. However, the original function was a 6th degree polynomial (if you have multiplied it all out), but the solution you posted is a 20th degree polynomial. That's clearly wrong.
$\displaystyle f(x)=3x^2(5-x)^4$
$\displaystyle f'(x)=\frac{d}{dx}[3x^2]*(5-x)^4+3x^2\frac{d}{dx}[(5-x)^4]$
$\displaystyle f'(x)=6x(5-x)^4+3x^2[4(5-x)^3*(-1)]$
$\displaystyle f'(x)=6x(5-x)^4-12x^4(5-x)^3$
Now, we can factor $\displaystyle 6x(5-x)^3$
$\displaystyle f'(x)=6x(5-x)^3[(5-x)-2x^3]$
exc...