Question 316781
Hi Nick, 

This is a good question. I have to ask you what background you have in calculus. In particular, are you familiar with the power rule? Chain rule, product rule, derivative of exponential and logarithmic functions? 

The power rule is very simple. The derivative of {{{x^n}}} is {{{n*x^(n-1)}}}. So the derivative of {{{x^6}}} is {{{6x^5}}}. The derivative of {{{x^4}}} is {{{4x^3}}}. The derivative of {{{1}}} is the same as the derivative of {{{x^0}}} which is {{{0*x^(-1)}}} which is {{{0}}}. 

So to answer your question, the derivative of {{{x^6 + x^4 + 1}}} is simply {{{6x^5 + 4x^3 + 0}}}. 

Now there are various ways to prove the power rule, and I would really like for you to see one. Merely memorizing a formula says nothing about our knowledge of mathematics. This is why I asked about your background, because if you have the right preparation already, the proof can be easy. If you do not have this preparation, it is not difficult to develop. 

-Mo