Mathematics 21 Online
OpenStudy (anonymous):

given t(x)=2sec(x)-4cos(x), what is t'(x)?

OpenStudy (eyust707):

here we want the derivative of the function

OpenStudy (eyust707):

don't let the notation scare you t(x) is basically the same as f(x)

OpenStudy (anonymous):

Alright so when finding the derivitive what do i do first?

OpenStudy (eyust707):

do each term separate

OpenStudy (eyust707):

first ind the derivative of sec(x)

OpenStudy (eyust707):

that is something that is usually just memorized.. is probably in a table in the front or back of your book

OpenStudy (anonymous):

secxtanx

OpenStudy (eyust707):

yep =)

OpenStudy (anonymous):

then what?

OpenStudy (eyust707):

and the second term?

OpenStudy (anonymous):

-sinx

OpenStudy (anonymous):

so so far we have 2secxtanx+4cosx?

OpenStudy (anonymous):

now what?

OpenStudy (eyust707):

perfect thats it!

OpenStudy (eyust707):

some people might dx in each term to show the chain rule.. but its usually not necessary

OpenStudy (anonymous):

how would i do that?

OpenStudy (eyust707):

well have you learned the chain rule yet?

OpenStudy (anonymous):

Yes...but i dont understand it.

OpenStudy (eyust707):

ok lets suppose we have this function: [f(x)= \sin (5x^2)\]

OpenStudy (eyust707):

$f(x)=\sin(5x^2)$

OpenStudy (anonymous):

Okay.

myininaya (myininaya):

t'(x)=2sec(x)tan(x)+4sin(x)

myininaya (myininaya):

so its not cos(x) its sin(x)

OpenStudy (eyust707):

first you take the derivative of the outside $\cos(5x^2)$ then you times it by the derivative of whats on the inside $\cos(5x^2)(10x)$

myininaya (myininaya):

since derivative of -4cos(x) is -4(-sin(x))=4sin(x)

OpenStudy (eyust707):

ahh yes your right myiniay missed that

OpenStudy (anonymous):

I got it! Finally...its only been 3 weeks.

OpenStudy (eyust707):

yayy

OpenStudy (eyust707):

its really not that bad once you get it.. some people just try to make over complicate it just remember this: "take the derivative of what on the outside and times it by the derivative of whats on the inside"

OpenStudy (anonymous):

its just hard to remmeber that the outside includes the inside.

OpenStudy (eyust707):

yeaa dont touch the inside at first

OpenStudy (eyust707):

gotta do the inside separate

OpenStudy (eyust707):

want to try another one? that uses the chain rule?

OpenStudy (anonymous):

sure! but other people keep answering them before i can even read the whole problem!!!

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