wondering if someone will walk me through how to do this problem:

Question

anonymous · Answer

Use the appropriate rule or combination of rules to find the derivative of the function defined below.
$$y=\sec^2(t^2-1)$$

hartnn · Answer

first can u find the derivative of sec^2 x ?

anonymous · Answer

sec^2tan^2

anonymous · Answer

well to the power of 2x i guess.

hartnn · Answer

to the power of 2x ? 
u know chain rule, right ? 
what is derivative of x^2 first ?

anonymous · Answer

2x

anonymous · Answer

1/2rootx

hartnn · Answer

its 2x, right, so derivative of sec^2 x = ?

anonymous · Answer

2x(sec)*(sec2xtan2x) ??

hartnn · Answer

applying chain rule, u get $(sec^2x)' = 2sec\: x(sec\: x)'=2sec \:x(sec\:xtan\:x)$
got this ?

anonymous · Answer

yes i got it.

hartnn · Answer

so now can u apply chain rule again and find it for your question ?

anonymous · Answer

i was just confused how you just had sec^2x wrote down is all, i thought you meant to the power of 2x, not sec^2(x)

hartnn · Answer

oh, sorry for confusion again....

anonymous · Answer

haha its okay, theres just no x's present in the question is all.

anonymous · Answer

so now i have: $$\sec^2(2t)+(t^2-1)(2)(\sec^2)(sectan)$$

hartnn · Answer

how sec^2 2t? 
the angle doesn't change...

anonymous · Answer

im using the product rule.

hartnn · Answer

$[sec^2(t^2-1)]'= 2sec (t^2-1)[sec(t^2-1)]'$
got this step ?

anonymous · Answer

yup/

hartnn · Answer

now next step would be ?

anonymous · Answer

to use thechain rule on [sec(t2−1)

hartnn · Answer

yes. try it out.

anonymous · Answer

sectan(t^2-1)(2t) ??

hartnn · Answer

yes! 
precisely it would be sec(t^2-1)tan(t^2-1)(2t)

hartnn · Answer

so final answe would be ?

anonymous · Answer

so now i have: $$2\sec(t^2-1)*\sec(t^2-1)\tan(t^2-1)(2t)$$

hartnn · Answer

correct!
 than can be simplified to $2\sec^2(t^2-1)*\tan(t^2-1)(2t)$

hartnn · Answer

$4t\sec^2(t^2-1)*\tan(t^2-1)$

anonymous · Answer

so that's my final answer? : )

hartnn · Answer

yup.
any doubts ?

hartnn · Answer

but, did u get all steps ?

anonymous · Answer

can i write that as: $$4t*\sec(t^2-1)^2*\tan(t^2-1)$$

anonymous · Answer

i wrote them all down : ) i get them now, it's not as hard when i got someone explaining it to me hah.

anonymous · Answer

can i write it like that though???

hartnn · Answer

yup.

anonymous · Answer

should there be a *t at the end of the equation?