## bmelyk 3 years ago wondering if someone will walk me through how to do this problem:

1. bmelyk

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

2. hartnn

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

3. bmelyk

sec^2tan^2

4. bmelyk

well to the power of 2x i guess.

5. hartnn

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

6. bmelyk

2x

7. bmelyk

1/2rootx

8. hartnn

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

9. bmelyk

2x(sec)*(sec2xtan2x) ??

10. hartnn

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

11. bmelyk

yes i got it.

12. hartnn

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

13. bmelyk

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)

14. hartnn

oh, sorry for confusion again....

15. bmelyk

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

16. bmelyk

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

17. hartnn

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

18. bmelyk

im using the product rule.

19. hartnn

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

20. bmelyk

yup/

21. hartnn

now next step would be ?

22. bmelyk

to use thechain rule on [sec(t2−1)

23. hartnn

yes. try it out.

24. bmelyk

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

25. hartnn

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

26. hartnn

so final answe would be ?

27. bmelyk

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

28. hartnn

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

29. hartnn

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

30. bmelyk

so that's my final answer? : )

31. hartnn

yup. any doubts ?

32. hartnn

but, did u get all steps ?

33. bmelyk

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

34. bmelyk

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

35. bmelyk

can i write it like that though???

36. hartnn

yup.

37. bmelyk

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