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

[jrjack]

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.

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

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?

 

[physicsnewb7]

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)...

 

[jrjack]

That makes more sense.

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

 

[physicsnewb7]

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

 

[jrjack]

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

Thanks.

 

[Mark44]

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.

 

[jrjack]

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