Question

Calculate the derivatives of the following real functions by using
the chain rule; maybe several times. In each case, determine the inner and outer
function to be used, together with their respective areas of definition.

a)\(h(x) = sin(cos(x))\)

Answer 1

outside first then inside
-cos(cos(x))sin(x)

Answer 2

understand?

Answer 3

hmm can you help me more zzrOck? i am noob at mathematics..

Answer 4

and your ding calc?

Answer 5

well we take the derivative of the outside function d(sin(x))/dx = cos(x) but we leave whats on the inside inside the derivative so cos(cos(x)) then we multiply it by the derivative of the inside function(this is the chain rule) inside function derived is d(cosx)/dx = -sinx so we have -cos(cosx)sinx

Answer 6

aah ok, and as conclusion we get -cos(cosx)sinx..?

Answer 7

we dont need to add anything more?

Answer 8

correct there is no product rule here if it where (sinx)(cosx)
we would

Answer 9

ok thank you very much zzrOc3r

Answer 10

np is it making since? what is the derivative of (3x+2)^2?

Answer 11

unfortunately not...

Answer 12

sorry for spelling I do this on a phone:) and sometimes just assume auto correct got it right:)

Answer 13

ok with the example I just gave (3x+2)^2 what is the outside function?

Answer 14

have you learned about composite functions?

Answer 15

np :) hmm i try to understand and calculate

Answer 16

i learned but it was long ago, and this year i am not going to university, i try to learn at home..

Answer 17

actually to be honest i am not started to learn, but next month i have exam, very soon i must started to learn it very serious

Answer 18

if f(x) = x^2 and g(x) = 3x+2 then, f composite g = f(g(x)) = (3x+2)^2. What we did here was take one function(g) and made it the input of the other function(f) so anyplace I saw a x in x^2 i put (3x+2) this is what is going on with the chaine rule. Our outside function is the funtion that "feeds" on the other. So our outside function on (3x+2)^2 is x^2 and the inside function is 3x+2 so to do d(f(g(x)))/dx = d((3x+2)^2)/dx we take the derivative of the outside function which is x^2 and get 2x, but we leave what is on the inside so we get 2(3x+2) but now we need to use the chaine rule and multiply what we have by the derivative of the inside so we have 2(3x+2)*d(3x+2)/dx = 2(3x+2)*3 =
6(3x+2)

Answer 19

ok..

Answer 20

in your situation let f(x) = sinx and g(x) = cosx so f composite g = f(g(x)) = sin(cosx) then we do the same thing take the dervative of f(x) which is cosx but leave the inside so cos(cosx) and multiply by the derivative of g(x) the inside part so cos(cosx)*d(cosx)/dx = cos(cos(x))*-sinx = -cos(cos(x))sin(x)

Answer 21

ok im done if you got any questions just ask:)

Answer 22

thank you zzrOc3r very much, for detailed explanation, it s really well explained, it helps me much

Answer 23

wait i look it deeply once more

Answer 24

if you want to do another one of your problems just paste it

Answer 25

zzrOck3r i have some questions but it will take time now, i need to do today 6-7 questions to deliver homework, but in next weeks if you will be here i will catch you to ask detailed questions, its very important for my exam, and exact this kind of question will come in exam

Answer 26

thank you, but i have other questions to be solved, if you are interested you are welcome

Answer 27

np zbrooks@pdx.edu I check it many times a day. I tudor this class and run a lab on it so its pretty fresh:)

Answer 28

cool, i will send you a message now to your email so that i dont loose your email ;)

Answer 29

i feel strong for my Exam thank to open study, here so many people who likes to help for math