Question

find y' : y = sin (x+y) ( i have the answer but i need the solution thanks)

Answer 1

Implicit differentiation\[y = \sin \left( x + y \right)\]Differentiate both side wrt \(x\)\[\frac{ dy }{ dx } = \frac{ d }{ dx } \sin \left( x+y \right)\]Chain rule\[\frac{ dy }{ dx } = \cos \left( x + y \right) \left( 1 + \frac{ dy }{ dx } \right)\]Expand right hand side and solve for \(\frac{dy}{dx}\)

Answer 2

damn chain rule! thanks. hey can you show me how you would expand the right hand side? i was told i need to put all the dy/dx on one side etc etc. may you show me how would you do it thanks

Answer 3

and i have another question if you dont mind. haha. but it can be for later. haha

Answer 4

Sure. \[\frac{ dy }{ dx } = \cos(x + y)\left( 1 + \frac{ dy }{ dx } \right)\]\[\frac{ dy }{ dx } = \cos \left( x + y \right) + \frac{ dy }{ dx }\cos \left( x + y \right)\]\[\frac{ dy }{ dx } - \frac{ dy }{ dx }\cos \left( x + y \right) = \cos \left( x + y \right)\]\[\frac{ dy }{ dx }\left( 1-\cos \left( x+y \right) \right) = \cos \left( x + y \right)\]Can you take it from here?

Answer 5

ooh! yes yes thanks i see it now. wait i have to ask, can i, in a way, 'adjust' the first equation given? or is it to be differentiated as it was?

Answer 6

Not that I'm aware of. I think the problem is for you to practice implicit differentiation just as it is given.

Answer 7

ok. thanks again!

Answer 8

You're welcome