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Calculus/sorry to ask ANOTHER

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Expert: - 4/8/2008


Question
to compute the 99th derivative of a trigonometric function, would i just
continue to take the derivative until I see a pattern?  I am a little confused on
how to figure out what number to divide by;

this is confusing, o i will elaborate a little.  I understand that when taking the
25th derivative of f(x)=cos(2x), once I get to the fourth derivative I stop, and
then break down 25=4*6 with a remainder of one.

how does work with 99?

Answer
You've noticed the pattern - the 4th, 8th, 12th, 16th, 20th, ... 88th, 92nd, 96th derivatives hae a cos(2x) in them.  

What goes out front should be determined, though.  The first derivative gives a 2 out front, the second gives a 4 out front, the third gives an 8 out front, etc.  Recognize that as being times 2 each time?  It's the chain rule.

Thanks for the question and have a great day.  Hope this works for you!

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