Question

Guys I give medals help me
find the y' of y=cos(x+y)

Answer 1

chain rule again for this one, in the guess of "implicit diff"

Answer 2

think of it as
\[f(x)=\cos(x+f(x))\]

Answer 3

then via the chain rule you get
\[f'(x)=-\sin(x+f(x))\times \left(1+f'(x)\right)\] solve this equation for \(f'(x)\)

Answer 4

of course it is easier to write
\[y'=-\sin(x+y)(1+y')\] and solve for \(y'\)

Answer 5

yeah, can I divide the y'+1 from one side to the other?

Answer 6

ok I got it

Answer 7

i will leave the algebra to you , but no, that is not how you solve
you need to distribute first

Answer 8

I got

Answer 9

i just remembered my algebra stuff.. thank you again

Answer 10

looks good to me

Answer 11

yeah just because you are taking calc doesn't mean the algebra has changed any
if my experience algebra is the biggest pitfall, not the ideas of calculus