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

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.

$$f^{(39)}(\pi/2)=$$

## 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???

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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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That makes more sense.

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

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

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

Thanks.

Mark44
Mentor

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.

Thanks for the clarity. Yes for this equation x = pi/2.