Question

DERIVATIVES
find the derivative of

Answer 1

\[\sin (\cos^{-1}x )\]

Answer 2

this is what i got so far

Answer 3

let u = cos^-1x

Answer 4

thus you have sin(u)

Answer 5

take the derivative of sin(u) which is cos(u)

Answer 6

\[- \frac{ \cos (\cos^{-1} x) }{ \sqrt{1-x^2} }\]

Answer 7

oh that's the original problem

Answer 8

the original problem is in the first comment. this one was my answer

Answer 9

ohh substitution

Answer 10

yes

Answer 11

dy/dx = dy/du*du/dx

Answer 12

you lost me

Answer 13

cos^-1 x = 1/cosx

Answer 14

1/cosx = sec x

Answer 15

so cos^-1x=1/cosx?

Answer 16

if i let u = arccosx then what would you do for du?

Answer 17

so

Answer 18

so du = 1/sqr(1-x^2) right?

Answer 19

alright then

Answer 20

thanks

Answer 21

my trig is a little shaky

Answer 22

sorry dude - you're right: https://math.berkeley.edu/~peyam/Math1ASu11/Handouts/Inverse%20Trig.pdf

Answer 23

hope that helps - i gotta review my trigonometry

Answer 24

yeah lol my trig is shaky too.
alright, so what would du be?

Answer 25

sorry im trying to study for a final on thursday and this type of problems are driving me crazy

Answer 26

its ok - you're learning...and i'm learning too - lol!

Answer 27

wouldnt it be easier to solve this using the chain rule? derivative of sin(arccosx) * derivative of arccos x times derivastive of x which is one... ?

Answer 28

-1/(1-x^2)^1/2

Answer 29

thats what you got?

Answer 30

the is the derivative of the inverse cosine

Answer 31

by subtitution? the book says is right but x instead of 1 tho

Answer 32

yeah

Answer 33

http://www.math.brown.edu/utra/trigderivs.html

Answer 34

i know them

Answer 35

so du = -1/(1-x^2)^1/2

Answer 36

thats why i was saying u=arccosx and du=1/(1-x^2)^1/2

Answer 37

yeah

Answer 38

yes and yes - sorry for he confusion

Answer 39

its all good

Answer 40

use the chain rule

Answer 41

so cos(u) du? du doesnt fit into it tho, does it?

Answer 42

one sec

Answer 43

i meant sin(u) brb let me work it out

Answer 44

so i got sin(u). then chain rule to get cos(u) *1.. ?

Answer 45

ok so that is the right answer - the answer you gave the first time

Answer 46

the book says the denominator is supposed to be x tho thats why i was confused

Answer 47

this is what the book has:
\[-\frac{ x }{ \sqrt{1-x^2} }\]

Answer 48

i just took a picture

Answer 49

i'm gonna post right now

Answer 50

there

Answer 51

oh i get it now. thanks!!!!!

Answer 52

:D

Answer 53

a detailed explanation via a photo

Answer 54

really helped thanks dude

Answer 55

yeah pictures are just better lol

Answer 56

np - anytime...i learned something too in the process so thank you too!

Answer 57

cool cool