A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Calculus HELP!
find the derivative of the function.
g(t)=5cos^3(times pie)(times t)
anonymous
 4 years ago
Calculus HELP! find the derivative of the function. g(t)=5cos^3(times pie)(times t)

This Question is Closed

zepp
 4 years ago
Best ResponseYou've already chosen the best response.0\(\large g(t) = 5cos^3(\pi t)\)

ksaimouli
 4 years ago
Best ResponseYou've already chosen the best response.0HINT  pie and t are constant

ksaimouli
 4 years ago
Best ResponseYou've already chosen the best response.0use the trig formulas for derivatives

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0where do i take the derivative first for this function?

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1Take 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.

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.1use the chain rule , not the product rule

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so whta rule would i be using in this case when i take ther derivative of the outermost function

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1The power rule :) and then as Unkle mentioned, the chain rule after that.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok..... so using the power rule in order to find the outermost function first this would be 15?

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1\[15(\cos(\pi t))^2 * (d/dt)(\cos(\pi t))\] 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.

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.1\[(f\circ h)'(x)=f(h(x))'=f'(h(x))\cdot h'(x)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok i got this step now i must find the derivative of (cos(piet))^2 right?

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1Don't look at the square anymore. You already dealt with that outermost function. the inner function is cos(pi t)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so i find the derivative of that and that is sin(piet) right?

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1\[15(\cos(\pi t))^2*(\sin(\pi t))*(d/dt)(\pi t)\] Good! now we have one last step. there is an inner inner function that you need to differentiate still, as I have written above.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok! thanks! ummm... would this be no wait u lost me

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1The innermost function is (pi t). So you need to multiply by the derivative of that :D Find the derivative! :D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0u see i thought of that being the answer but i wasn't quite sure... umm okay so the derivative of piet is just piet?

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1\[(d/dt)(\pi t)=\pi(d/dt)t=?\]

zepp
 4 years ago
Best ResponseYou've already chosen the best response.0\(\pi\) is a constant, and when a constant combined to a variable, the variable goes to 1 but the constant stay.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0im sorry u guys lost me completely

zepp
 4 years ago
Best ResponseYou've already chosen the best response.0Let's restart everything, haha

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1nooo don't get lost :D you were so close!

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.1\[g(t) = 5\cos^3(\pi t)\] \[f(x)=5\cos^3(x)\] \[h(x)= \pi x\]

zepp
 4 years ago
Best ResponseYou've already chosen the best response.0Okay, \[\large g(t) = 5cos^3(\pi t)\]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 \[3*5(cos^2(\pi t))*\frac{d}{dt}cos^2(\pi t)*\frac{d}{dt}(\pi t)\]

zepp
 4 years ago
Best ResponseYou've already chosen the best response.0\(\large 3*5(cos^2(\pi t))*\frac{d}{dt}cos(\pi t)*\frac{d}{dt}(\pi t)\)*** Sorry

zepdrix
 4 years ago
Best ResponseYou've already chosen the best response.1what 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok !!!! i think i got!!! THANKS SOOOOO MUCH I WAS HAVING TROUBLEE!!!!!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.