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
Follow Math Help Forum on Facebook and Google+
Originally Posted by curlywurlysqurly 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 differentiate? Dx[sec^2 x] = 2(sec x)(sec x tan x) = 2(sec^2 x)(tan x) you just nid to apply chain rule.
sorry but i don't understand how you did that!!! where did the tan x come from???
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?
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?
You know that $\displaystyle \sec x=\frac1{\cos x}$ Now $\displaystyle \Big[(\cos x)^{-1}\Big]'=-(\cos x)^{-2}\cdot(\cos x)'.$ So, $\displaystyle \frac{\sin x}{\cos^2x}=\frac1{\cos x}\cdot\frac{\sin x}{\cos x}.$
okay thanks i get it now! thankyou all for your help!!!! xxx
View Tag Cloud