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lilly21

  • 2 years ago

Calculus HELP! find the derivative of the function. g(t)=5cos^3(times pie)(times t)

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  1. zepp
    • 2 years ago
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    \(\large g(t) = 5cos^3(\pi t)\)

  2. ksaimouli
    • 2 years ago
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    HINT - pie and t are constant

  3. ksaimouli
    • 2 years ago
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    use the trig formulas for derivatives

  4. lilly21
    • 2 years ago
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    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
    • 2 years ago
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    where do i take the derivative first for this function?

  6. zepdrix
    • 2 years ago
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    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
    • 2 years ago
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    use the chain rule , not the product rule

  8. lilly21
    • 2 years ago
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    ok so whta rule would i be using in this case when i take ther derivative of the outermost function

  9. zepdrix
    • 2 years ago
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    The power rule :) and then as Unkle mentioned, the chain rule after that.

  10. lilly21
    • 2 years ago
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    ok..... so using the power rule in order to find the outermost function first this would be 15?

  11. zepdrix
    • 2 years ago
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    \[15(\cos(\pi t))^2 * (d/dt)(\cos(\pi t))\] 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
    • 2 years ago
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    \[(f\circ h)'(x)=f(h(x))'=f'(h(x))\cdot h'(x)\]

  13. lilly21
    • 2 years ago
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    ok i got this step now i must find the derivative of (cos(piet))^2 right?

  14. zepdrix
    • 2 years ago
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    Don't look at the square anymore. You already dealt with that outermost function. the inner function is cos(pi t)

  15. lilly21
    • 2 years ago
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    ok so i find the derivative of that and that is -sin(piet) right?

  16. zepdrix
    • 2 years ago
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    \[15(\cos(\pi t))^2*(-\sin(\pi t))*(d/dt)(\pi t)\] 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
    • 2 years ago
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    ok! thanks! ummm... would this be no wait u lost me

  18. zepdrix
    • 2 years ago
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    The innermost function is (pi t). So you need to multiply by the derivative of that :D Find the derivative! :D

  19. lilly21
    • 2 years ago
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    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
    • 2 years ago
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    \[(d/dt)(\pi t)=\pi(d/dt)t=?\]

  21. zepp
    • 2 years ago
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    \(\pi\) is a constant, and when a constant combined to a variable, the variable goes to 1 but the constant stay.

  22. lilly21
    • 2 years ago
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    zepdrix :[

  23. lilly21
    • 2 years ago
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    im sorry u guys lost me completely

  24. zepp
    • 2 years ago
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    Let's restart everything, haha

  25. zepdrix
    • 2 years ago
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    nooo don't get lost :D you were so close!

  26. lilly21
    • 2 years ago
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    is it just pie?

  27. zepdrix
    • 2 years ago
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    yayyyy \:D/

  28. zepdrix
    • 2 years ago
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    pi* lol

  29. UnkleRhaukus
    • 2 years ago
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    \[g(t) = 5\cos^3(\pi t)\] \[f(x)=5\cos^3(x)\] \[h(x)= \pi x\]

  30. rainbow22
    • 2 years ago
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    CHAIN RULE :D

  31. zepp
    • 2 years ago
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    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
    • 2 years ago
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    ok how it pi though

  33. lilly21
    • 2 years ago
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    how is it pi

  34. zepp
    • 2 years ago
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    \(\large 3*5(cos^2(\pi t))*\frac{d}{dt}cos(\pi t)*\frac{d}{dt}(\pi t)\)*** Sorry

  35. zepdrix
    • 2 years ago
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    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
    • 2 years ago
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    ok !!!! i think i got!!! THANKS SOOOOO MUCH I WAS HAVING TROUBLEE!!!!!!

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