Why is the chain rule factor x not 2x in this arcsecant derivative?

[Puchinita5]

Homework Statement

I attached a problem from my homework.

My only issue is that I don't know why it is x arc sec and not 2x arc sec etc...shouldn't there be a 2x from the chain rule from the derivative inside the square root? I cannot understand for my life why there is an x and not a 2x.

I kept getting this wrong until I googled it and someone in yahoo answers gave a response without a 2, so i tried it and my online homework said it was right. But don't know why!

Homework Equations

The Attempt at a Solution

 

[Amok]

Well, I didn't get the same result, maybe I have to simplify it, but the 2 factor goes away because the 1/2 exponent "comes down" when you derive sqrt (x^2 - 1). Is that what you are talking about? And why are you talking about arcsec?

 

[Puchinita5]

Oh dear. That was a silly mistake! I definitely didn't bring down the 1/2 when I took the derivative. ::slaps forehead:: It's been a while since I took calc 1 so I am making a lot of really silly mistakes now in Calc 2!

I couldn't see for my life what I was missing!

Oh and I was saying arcsec because i thought sec^-1x was more confusing to read.

Thank you for your help!

 

[Amok]

1/sec = cos btw

 

[dextercioby]

Well

$$(\sec^{-1} x)' = \frac{1}{x\sqrt{x^2 -1}}$$

so that explains the first term. As for the second, there's no 2, because of the chain rule.