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18.) Find the 65th derivative of sin(x) by finding the first few derivatives and observing the pattern that occurs. (sin(x))(65)=?
3 Answers
- ?Lv 52 years ago
sin x goes to cos x which goes to - sin x which goes to - cos x and then the cycle restarts at sin x.
so there are 4 events in this cycle.
1) sin x
2) cos x
3) - sin x
4) -cos x
you want the 65th. you know 64 goes into 4, 16 times. so thats 16 complete cycles.
so the 65th would be the start again.
- Steve ALv 72 years ago
First derivative = cos(x)
Second derivative = -sin(x)
Third derivative = -cos(x)
Fourth derivative = sin(x)
See the pattern?
How many times does it repeat by the 65th derivative?
- rotchmLv 72 years ago
Did you at lest try their suggestion?
And again, *you* must learn by heart the derivative of the basic functions. We cant learn by heart for you.
So, whats the derivative of sin(x) ?
Then, the derivative of the above answer?
Then the derivative of that answer?
Etc... do it a few more times.
See the pattern?
Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.