Question

Find dy/dx for y(x) given via cos(y) = y + exp(x)

Answer 1

use chain rule,

\(\dfrac{d}{dx} f(y) = f'(y) \dfrac{dy}{dx} \)

Answer 2

so what will be
d/dx (cos y) ?

Answer 3

-sin(y)

Answer 4

WOW yuor very good @hartnn

Answer 5

just -sin y ?

Answer 6

Is it 1/-sin(y) because its in terms of d/dx?

Answer 7

no...use of chain rule
f'(y) dy/dx

so
it will be
-sin y dy/dx

got this ?

Answer 8

yes dy/dx = dy/du * du/dx right?

Answer 9

correct

so, any doubts for

d/dx (cos y) = -sin y dy/dx
??

Answer 10

No I can see that now, so would exp(x) differentiate into exp(x)dx/dy?

Answer 11

e^x is the function of x only

no chain rule

d.dx e^x = e^x

Answer 12

d/dx e^x = e^x

Answer 13

I am really lost here but, the overall equation would be differentiated to
-sin(y) * dy/dx = e(x) ?

Answer 14

what about the 'y'
?

-sin y dy/dx = dy/dx + e^x

Answer 15

oh of course, I just assumed because you differentiate y to 0, then 0* dy/dx would that not just remove it?

Answer 16

ignore that I just realised the mistake i made y differentiates to 1

Answer 17

no,

d/dx(y) = dy/dx

y is not a constant

Answer 18

but do you not have to do anything with the -sin(y) dy/dx? dont you have to evaluate the dy/dx part?

Answer 19

you need dy/dx right ?

you can get it from
-sin y dy/dx = dy/dx + e^x

try isolating
dy/dx

Answer 20

dy/dx - (dy/dx)/-sin(y) = e(x) / -sin(y)

Answer 21

-sin y dy/dx = dy/dx + e^x

-sin y dy/dx - dy/dx = e^x

dy/dx (-sin y -1) = e^x

dy/dx = -e^x/ (1+sin y)

like that ^^

Answer 22

wow, thank you for all the help, my algebra and differentiation is incredibly rusty as I have been studying computer science so this has been a nice refresher, thank you :)

Answer 23

welcome ^_^
oh and since you're new here
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