Hi, would someone please tell me how to differentiate sec^2 x?

I tried it and got (-4sin2x)/(cos2x+1)^2

Not sure if that is right tho

xxx

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- Oct 27th 2007, 06:03 AMcurlywurlysqurlyDifferentiating sec
Hi, would someone please tell me how to differentiate sec^2 x?

I tried it and got (-4sin2x)/(cos2x+1)^2

Not sure if that is right tho

xxx - Oct 27th 2007, 07:08 AMkalagota
- Oct 28th 2007, 03:14 AMcurlywurlysqurly
sorry but i don't understand how you did that!!!

where did the tan x come from??? - Oct 28th 2007, 09:41 AMKrizalid
Do you know what chain rule is?

$\displaystyle f(x)=\sec^2x.$

To take its derivative, we use $\displaystyle (u^n)'=nu^{n-1}\cdot u'.$

So, $\displaystyle f'(x)=2\sec x\cdot(\sec x)'.$

Does that make sense? - Oct 28th 2007, 10:19 AMcurlywurlysqurly
yea thats all fine, but how do u differentiate sec x? is it just a standard result or is there some way to do it?

- Oct 28th 2007, 10:25 AMKrizalid
You know that $\displaystyle \sec x=\frac1{\cos x}$

Now $\displaystyle \Big[(\cos x)^{-1}\Big]'=-(\cos x)^{-2}\cdot(\cos x)'.$

So, $\displaystyle \frac{\sin x}{\cos^2x}=\frac1{\cos x}\cdot\frac{\sin x}{\cos x}.$ - Oct 28th 2007, 11:03 AMcurlywurlysqurly
okay thanks i get it now!

thankyou all for your help!!!!

xxx