Asked by Anonymous
find the derevative (hint try to use limits)
(x^2010 - 1 )\(x -1 )
(x^2010 - 1 )\(x -1 )
Answers
Answered by
Marth
already answered (separate topic)
Answered by
drwls
Using the L'Hopital limit theorem (at x = 1) will not help you compute the derivative for arbitrary values of x.
The quotient function can be rewritten,
x^2009 + x^2008 + ...+ x^2 + x + 1
I had to leave out 2005 different terms. you then differentiate that and get a long string of terms.
You can also get a shorter expression for the derivative by using the formula for the derivative of the ratio of two functions.
f'(x) = [2010x^2009*(x-1) - x^2010]/(x-1)^2
= 2010*x^2009/(x-1) - x^2010/(x-1)^2
The quotient function can be rewritten,
x^2009 + x^2008 + ...+ x^2 + x + 1
I had to leave out 2005 different terms. you then differentiate that and get a long string of terms.
You can also get a shorter expression for the derivative by using the formula for the derivative of the ratio of two functions.
f'(x) = [2010x^2009*(x-1) - x^2010]/(x-1)^2
= 2010*x^2009/(x-1) - x^2010/(x-1)^2
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