## v.s 3 years ago Differentiate with respect to t. y = b cos t + t2 sin t

1. Shriya

sin t (2-b) + 2t cos t

2. v.s

- sint

3. Chlorophyll

( cost)' ? (sint)' ?

4. Chlorophyll

-> b ( cos t ) ' = - bsint Okie, so far?

5. v.s

okayy

6. v.s

y' = -bsin+2tcos

7. Shriya

y=bcost+t2sint differentiating w.r.t t, dy/dt= -bsint+ d/dt(2tsint) now, we have to differentiate 2tsint using product rule for derivative. so, the derivative of 2tsint becomes (2tcost+2tsint) therefore, dy/dt= -bsint+2tsint+2tcost taking sint common, dy/dx=sint(2-b)+2tcost

8. v.s

i got it wrong

9. v.s

but i understand what you did

10. Shriya

datz ok! :) not a big deal. derivatives is realy easy as compared to the other sections of calculus. u jus need 2 know the ways to differentiate! :)

11. v.s

yeaaa thank you :)

12. Chlorophyll

Apply product rule here ( t²* sin t ) ' with : u = t² --> u' = ... v = sint --> v' = ....

13. Chlorophyll

@v.s Do you know product rule?

14. v.s

yes

15. v.s

2t*sint + cost*t^2

16. Chlorophyll

Yep, now put the 2 results together :) y' = ....

17. Chlorophyll

y = b cos t + t² sin t ->y' = ...

18. v.s

y"= -bcost+2t*sint+cost*t^2

19. Chlorophyll

y = b cos t + t² sin t -> b ( cos t ) ' = - bsint -> ( t² sin t )' = 2t sint+ t² cost

20. v.s

you just put them together

21. v.s

- bsint + 2t sint+ t² cost

22. Chlorophyll

What's my instruction above?

23. v.s

product rule?

24. Chlorophyll

The product rule applied to take derivative of the second term!

25. v.s

i'm confused

26. Chlorophyll

y = b cos t + t² sin t -> b ( cos t ) ' = - bsint ( derivative of the first term) -> ( t² sin t )' = 2t sint+ t² cost ( derivative of the second term)

27. v.s

what do you do next?

28. Chlorophyll

Yep, now put the 2 results together :) y = b cos t + t² sin t y' = - bsint + 2t sint+ t² cost

29. Chlorophyll

Now you can make it neat by simplifying - bsint + 2t sint together.

30. v.s

okaay thnks you