I don't understand the meaning of f^(39)(pi/2)?

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I don't understand the meaning of f^(39)(pi/2)??

Homework Statement



Find the indicated derivative of f(x)=sin x and evaluate it at x=pi/2.

[tex]f^{(39)}(\pi/2)=[/tex]

Homework Equations





The Attempt at a Solution



I'm not sure what the f^39 means??? And it could be f(39)(pi/2)??? but it looks like f raised to the 39th power???

Is this a common way to express a problem, because I have not seen one like this yet?

I know the derivative of sin x, is cos x, and if x=pi/2, then cos(pi/2)=0

But how should I evaluate the rest of this problem?
If f^(39) makes no sense, then f(39)(pi/2) doesn't make any sense, because x=pi/2???
 

Answers and Replies

  • #2


I think they mean take the 39th derivative of sin(x) and evaluate that at pi/2 the 2nd derivative -sin(x) third is -cos(x) and fourth is sin(x)......
 
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  • #3
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That makes more sense.

Is there a short cut or should I just change sin and cos (including the negative) 39 times?
 
  • #4


That makes more sense.

Is there a short cut or should I just change sin and cos (including the negative) 39 times?
every fourth derivative gives you sin(x) I think you can take it from there
 
  • #5
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Yes, as I started doing it, I quickly saw sin x after 4 times, and ended up with -cos x = 0.

Thanks.
 
  • #6
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Yes, as I started doing it, I quickly saw sin x after 4 times, and ended up with -cos x = 0.

Thanks.
That's the right value, but what you got was -cos(π/2) = 0.

The notation f(39)(x), with parentheses around the exponent, usually means the derivative of that order. Without parentheses it would just mean raising the function to the indicated power.
 
  • #7
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Thanks for the clarity. Yes for this equation x = pi/2.
 

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