## lilly21 Group Title Calculus HELP! find the derivative of the function. g(t)=5cos^3(times pie)(times t) one year ago one year ago

1. zepp Group Title

$$\large g(t) = 5cos^3(\pi t)$$

2. ksaimouli Group Title

HINT - pie and t are constant

3. ksaimouli Group Title

use the trig formulas for derivatives

4. lilly21 Group Title

ok zepp so tell me if i have it right so far..... y(prime)=u(prime) times v+v(prime) times u = no wait.... im stuck

5. lilly21 Group Title

where do i take the derivative first for this function?

6. zepdrix Group Title

Take the derivative of the OUTERMOST function first. Trig functions can be a little tricky to read since the power is written in a different location. Identify the outermost function. $5(\cos(\pi t))^3$ That is another way it can be written so you can easily identify the outermost function.

7. UnkleRhaukus Group Title

use the chain rule , not the product rule

8. lilly21 Group Title

ok so whta rule would i be using in this case when i take ther derivative of the outermost function

9. zepdrix Group Title

The power rule :) and then as Unkle mentioned, the chain rule after that.

10. lilly21 Group Title

ok..... so using the power rule in order to find the outermost function first this would be 15?

11. zepdrix Group Title

$15(\cos(\pi t))^2 * (d/dt)(\cos(\pi t))$ good you got the first step :) by the chain rule, you must now multiply by the derivative of the inside, as I have written here.

12. UnkleRhaukus Group Title

$(f\circ h)'(x)=f(h(x))'=f'(h(x))\cdot h'(x)$

13. lilly21 Group Title

ok i got this step now i must find the derivative of (cos(piet))^2 right?

14. zepdrix Group Title

Don't look at the square anymore. You already dealt with that outermost function. the inner function is cos(pi t)

15. lilly21 Group Title

ok so i find the derivative of that and that is -sin(piet) right?

16. zepdrix Group Title

$15(\cos(\pi t))^2*(-\sin(\pi t))*(d/dt)(\pi t)$ Good! now we have one last step. there is an inner inner function that you need to differentiate still, as I have written above.

17. lilly21 Group Title

ok! thanks! ummm... would this be no wait u lost me

18. zepdrix Group Title

The innermost function is (pi t). So you need to multiply by the derivative of that :D Find the derivative! :D

19. lilly21 Group Title

u see i thought of that being the answer but i wasn't quite sure... umm okay so the derivative of piet is just piet?

20. zepdrix Group Title

$(d/dt)(\pi t)=\pi(d/dt)t=?$

21. zepp Group Title

$$\pi$$ is a constant, and when a constant combined to a variable, the variable goes to 1 but the constant stay.

22. lilly21 Group Title

zepdrix :[

23. lilly21 Group Title

im sorry u guys lost me completely

24. zepp Group Title

Let's restart everything, haha

25. zepdrix Group Title

nooo don't get lost :D you were so close!

26. lilly21 Group Title

is it just pie?

27. zepdrix Group Title

yayyyy \:D/

28. zepdrix Group Title

pi* lol

29. UnkleRhaukus Group Title

$g(t) = 5\cos^3(\pi t)$ $f(x)=5\cos^3(x)$ $h(x)= \pi x$

30. rainbow22 Group Title

CHAIN RULE :D

31. zepp Group Title

Okay, $\large g(t) = 5cos^3(\pi t)$We identified $$5cos(\pi t)$$ as the inner function, and $$(Stuffshere)^3$$ as the outter function, so we could apply the power rule here and we apply the chain rule $3*5(cos^2(\pi t))*\frac{d}{dt}cos^2(\pi t)*\frac{d}{dt}(\pi t)$

32. lilly21 Group Title

ok how it pi though

33. lilly21 Group Title

how is it pi

34. zepp Group Title

$$\large 3*5(cos^2(\pi t))*\frac{d}{dt}cos(\pi t)*\frac{d}{dt}(\pi t)$$*** Sorry

35. zepdrix Group Title

what is the derivative of 2x? its just 2 times the derivative of x. So you apply the power rule, (derivative of x^1 = 1.. so you end up with 2. :O yes? same thing is happening here. don't let the pi confuse you, its just a number

36. lilly21 Group Title

ok !!!! i think i got!!! THANKS SOOOOO MUCH I WAS HAVING TROUBLEE!!!!!!