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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
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

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zepp Group TitleBest ResponseYou've already chosen the best response.0
\(\large g(t) = 5cos^3(\pi t)\)
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
HINT  pie and t are constant
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
use the trig formulas for derivatives
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
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
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
where do i take the derivative first for this function?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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.
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
use the chain rule , not the product rule
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
ok so whta rule would i be using in this case when i take ther derivative of the outermost function
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
The power rule :) and then as Unkle mentioned, the chain rule after that.
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
ok..... so using the power rule in order to find the outermost function first this would be 15?
 one year ago

zepdrix Group TitleBest 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.
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
\[(f\circ h)'(x)=f(h(x))'=f'(h(x))\cdot h'(x)\]
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
ok i got this step now i must find the derivative of (cos(piet))^2 right?
 one year ago

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

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
ok so i find the derivative of that and that is sin(piet) right?
 one year ago

zepdrix Group TitleBest 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.
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
ok! thanks! ummm... would this be no wait u lost me
 one year ago

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

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
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?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[(d/dt)(\pi t)=\pi(d/dt)t=?\]
 one year ago

zepp Group TitleBest 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.
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
zepdrix :[
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
im sorry u guys lost me completely
 one year ago

zepp Group TitleBest ResponseYou've already chosen the best response.0
Let's restart everything, haha
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
nooo don't get lost :D you were so close!
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
is it just pie?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
yayyyy \:D/
 one year ago

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

rainbow22 Group TitleBest ResponseYou've already chosen the best response.0
CHAIN RULE :D
 one year ago

zepp Group TitleBest ResponseYou've already chosen the best response.0
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 \[3*5(cos^2(\pi t))*\frac{d}{dt}cos^2(\pi t)*\frac{d}{dt}(\pi t)\]
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
ok how it pi though
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
how is it pi
 one year ago

zepp Group TitleBest 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
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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
 one year ago

lilly21 Group TitleBest ResponseYou've already chosen the best response.0
ok !!!! i think i got!!! THANKS SOOOOO MUCH I WAS HAVING TROUBLEE!!!!!!
 one year ago
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