SOLUTION: Will someone please show me how to find the derivative of the following function: f(x) = x^6 + x^4 + 1 A solution with full working and steps would be much appreciated. Than

Algebra ->  Proofs -> SOLUTION: Will someone please show me how to find the derivative of the following function: f(x) = x^6 + x^4 + 1 A solution with full working and steps would be much appreciated. Than      Log On


   



Question 316781: Will someone please show me how to find the derivative of the following function:
f(x) = x^6 + x^4 + 1
A solution with full working and steps would be much appreciated.
Thanks -Nick.

Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
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%5En is n%2Ax%5E%28n-1%29. So the derivative of x%5E6 is 6x%5E5. The derivative of x%5E4 is 4x%5E3. The derivative of 1 is the same as the derivative of x%5E0 which is 0%2Ax%5E%28-1%29 which is 0.
So to answer your question, the derivative of x%5E6+%2B+x%5E4+%2B+1 is simply 6x%5E5+%2B+4x%5E3+%2B+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