Question

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

Answer 1

here we want the derivative of the function

Answer 2

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

Answer 3

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

Answer 4

do each term separate

Answer 5

first ind the derivative of sec(x)

Answer 6

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

Answer 7

secxtanx

Answer 8

yep =)

Answer 9

then what?

Answer 10

and the second term?

Answer 11

-sinx

Answer 12

so so far we have 2secxtanx+4cosx?

Answer 13

now what?

Answer 14

perfect thats it!

Answer 15

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

Answer 16

how would i do that?

Answer 17

well have you learned the chain rule yet?

Answer 18

Yes...but i dont understand it.

Answer 19

ok lets suppose we have this function:

[f(x)= \sin (5x^2)\]

Answer 20

\[f(x)=\sin(5x^2)\]

Answer 21

Okay.

Answer 22

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

Answer 23

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

Answer 24

first you take the derivative of the outside

\[\cos(5x^2)\]

then you times it by the derivative of whats on the inside

\[\cos(5x^2)(10x)\]

Answer 25

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

Answer 26

ahh yes your right myiniay missed that

Answer 27

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

Answer 28

yayy

Answer 29

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"

Answer 30

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

Answer 31

yeaa dont touch the inside at first

Answer 32

gotta do the inside separate

Answer 33

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

Answer 34

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