## jayshane Group Title DERIVATIVES OF TRIGO IDENTITIES no.1)Y=cos4 t- sin4 t=-2sin 2t INEED SOLUTION PLS....T_T NID BADLY!!!! one year ago one year ago

1. tkhunny Group Title

It makes no sense as it it presented. Trigonometric Identities are statements and the term "derivative" has no meaning for such a statement. Can you provide the exact wording of the problem?

2. jayshane Group Title

differentiate Y=cos4 t -sin4 t

3. kirbykirby Group Title

Is this cos(4t) or $\cos^4t$

4. tkhunny Group Title

We're looking for $$\dfrac{dY}{dt}$$? Can you find $$\dfrac{d}{dt}\cos^{4}(t)$$

5. jayshane Group Title

yes

6. tkhunny Group Title

What do you get for that?

7. jayshane Group Title

ist assingment dude

8. tkhunny Group Title

Conversation Overlap Misunderstanding... What do you get for $$\dfrac{d}{dt}\cos^{4}(t)$$

9. jayshane Group Title

its our assignment in differential calculus...

10. zepdrix Group Title

Jay you didn't answer the question kirby asked. Is it suppose to be $$\cos(4t)$$ or $$\cos^4(t)$$?

11. jayshane Group Title

the second one

12. jayshane Group Title

i dont know how to type that

13. kirbykirby Group Title

Just think of it as the chain rule. You can move the exponent if it confuses you: $\frac{d}{dt}\cos^4t=\frac{d}{dt}(\cos t)^4 = 4(\cos t)^3(-\sin t)$

14. kirbykirby Group Title

-sin t comes from the fact that it is the derivative of cos t by using the chain rule.

15. jayshane Group Title

the book has an answer of -2sin 2 t

16. kirbykirby Group Title

Just use the same logic on $\frac{d}{dt}\sin^4t=4\sin^3t(\cos t)$

17. jayshane Group Title

cos4t-sin4t= kirb can u give me the whole solution soo i can studied it... please

18. kirbykirby Group Title

so now: $-4\cos^3t(\sin t) - 4\sin^3t(\cos t) = -4\cos t*\sin t(\cos^t+\sin^2t)=-4\cos t*\sin t(1)$

19. kirbykirby Group Title

Now use the double-angle formula

20. kirbykirby Group Title

$Since : \sin(2t)=2\sin t \cos t$

21. kirbykirby Group Title

$-4\cos t \sin t = -2(2\cos t \sin t) = -2\sin(2t)$

22. jayshane Group Title

THANK YOU KIRB!!!

23. tkhunny Group Title

Since we're just doing your homework, I'd do it this way. $$\cos^{4}(t) - \sin^{4}(t) = [\cos^{2}(t) - \sin^{2}(t)][\cos^{2}(t) + \sin^{2}(t)] = \cos(2x)$$ It's a lot easier after that.

24. tkhunny Group Title

Sorry, not sure why I wrote 2x on the end, there. Should be 2t. If you are going to make me do ALL the work, you'll have to show me how that last step happened. There's a whole lot of stuff in there that magically turned into cos(2t).

25. kirbykirby Group Title

The method by tkhunny is also excellent :) It is shorter but I usually just do it "straight-forward" unless I'm stuck and tkhunny's method is a good trick to make the derivative a lot easier

26. tkhunny Group Title

I'm usually the brute force guy. Once in a while I see one!

27. kirbykirby Group Title

Hehe good one ;)

28. jayshane Group Title