Question

Find y' if y = cos(x + y). (5 points) 1. 0 2. 1 3. -sin(x + y) 4. the quotient of negative 1 times the sine of the quantity x plus y and 1 plus the sine of the quantity x plus y

Answer 1

4 )
`(d y)/(d x) = (-sin(x+y))/(1+sin(x+y))`

Explanation:

Given y = cos (x +y) ...(i)

we will use formula

`(d(cosx))/(dx) = - sinx`

Differentiating equation (i) with respective to 'x'

`(dy)/(dx) = - sin ( x+y) X (d)/(dx) (x +y)`

`(dy)/(dx) = - sin ( x+y) (1 + (d y)/(d x) )`

on simplification , we get

`(dy)/(dx) = - sin ( x+y) - (sin(x+y) (d y)/(d x) )`

`(dy)/(dx) + (sin(x+y) (d y)/(d x) ) = - sin (x +y)`

Taking common
`(dy)/(dx)`

`(1 + (sin(x+y)) (d y)/(d x) ) = - sin (x +y)`

`(d y)/(d x) = (-sin(x+y))/(1+sin(x+y))`