Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

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

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
\(\large g(t) = 5cos^3(\pi t)\)
HINT - pie and t are constant
use the trig formulas for derivatives

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

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
where do i take the derivative first for this function?
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.
use the chain rule , not the product rule
ok so whta rule would i be using in this case when i take ther derivative of the outermost function
The power rule :) and then as Unkle mentioned, the chain rule after that.
ok..... so using the power rule in order to find the outermost function first this would be 15?
\[15(\cos(\pi t))^2 * (d/dt)(\cos(\pi t))\] 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.
\[(f\circ h)'(x)=f(h(x))'=f'(h(x))\cdot h'(x)\]
ok i got this step now i must find the derivative of (cos(piet))^2 right?
Don't look at the square anymore. You already dealt with that outermost function. the inner function is cos(pi t)
ok so i find the derivative of that and that is -sin(piet) right?
\[15(\cos(\pi t))^2*(-\sin(\pi t))*(d/dt)(\pi t)\] Good! now we have one last step. there is an inner inner function that you need to differentiate still, as I have written above.
ok! thanks! ummm... would this be no wait u lost me
The innermost function is (pi t). So you need to multiply by the derivative of that :D Find the derivative! :D
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?
\[(d/dt)(\pi t)=\pi(d/dt)t=?\]
\(\pi\) is a constant, and when a constant combined to a variable, the variable goes to 1 but the constant stay.
zepdrix :[
im sorry u guys lost me completely
Let's restart everything, haha
nooo don't get lost :D you were so close!
is it just pie?
yayyyy \:D/
pi* lol
\[g(t) = 5\cos^3(\pi t)\] \[f(x)=5\cos^3(x)\] \[h(x)= \pi x\]
CHAIN RULE :D
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 \[3*5(cos^2(\pi t))*\frac{d}{dt}cos^2(\pi t)*\frac{d}{dt}(\pi t)\]
ok how it pi though
how is it pi
\(\large 3*5(cos^2(\pi t))*\frac{d}{dt}cos(\pi t)*\frac{d}{dt}(\pi t)\)*** Sorry
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
ok !!!! i think i got!!! THANKS SOOOOO MUCH I WAS HAVING TROUBLEE!!!!!!

Not the answer you are looking for?

Search for more explanations.

Ask your own question