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)

use formula for the circle a=3.14

step-by-step explanation:

none.

step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

tap for more

m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0