Question

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

Answer 1

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

Answer 2

HINT - pie and t are constant

Answer 3

use the trig formulas for derivatives

Answer 4

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

Answer 5

where do i take the derivative first for this function?

Answer 6

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.

Answer 7

use the chain rule , not the product rule

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

\[15(\cos(\pi t))^2 * (d/dt)(\cos(\pi t))\]
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.

Answer 12

\[(f\circ h)'(x)=f(h(x))'=f'(h(x))\cdot h'(x)\]

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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?

Answer 20

\[(d/dt)(\pi t)=\pi(d/dt)t=?\]

Answer 21

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

Answer 22

zepdrix :[

Answer 23

im sorry u guys lost me completely

Answer 24

Let's restart everything, haha

Answer 25

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

Answer 26

is it just pie?

Answer 27

yayyyy \:D/

Answer 28

pi* lol

Answer 29

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

Answer 30

CHAIN RULE :D

Answer 31

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
\[3*5(cos^2(\pi t))*\frac{d}{dt}cos^2(\pi t)*\frac{d}{dt}(\pi t)\]

Answer 32

ok how it pi though

Answer 33

how is it pi

Answer 34

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

Sorry

Answer 35

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

Answer 36

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