Find dy/dx if y=sin(x+y) steps would be appreciated.

Step-by-step explanation:

We have the function

We need find the derivative of y with respect to x

Note that the function depends on the variable x and the variable y. Therefore the derivative of y with respect to x will be equal to the derivative of by the internal derivative of  

Step-by-step explanation:

Note that y=sin(x+y) is an implicit function; y appears on both sides of the equation, which makes it difficult or impossible to solve for y.

However, our job here is to find the derivative dy/dx.

We apply the derivative operator d/dx to both sides.  Here are the results:

dy

= cos(x + y)(dx/dx + dy/dx), or

dx                                                         Note:  dx/dx = 1

dy

= cos(x + y)(1 + dy/dx), or  = cos(x + y) + cos(x + y)(dy/dx)

dx

We move that cos(x + y)(dy/dx) term to the left side to consolidate dy/dx terms:

dy

 -  cos(x + y)(dy/dx) = cos(x + y)

dx

or:

 dy

[ ] [ 1 -  cos(x + y) ] = cos(x + y)

  dx

Finally, we divide both sides by [ 1 -  cos(x + y) ], obtaining the derivative:

 dy            cos(x + y)

[ ]  

  dx         1 -  cos(x + y)

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step-by-step explanation: