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

Answer:

4 ) $\frac{d y}{d x} = \frac{-sin(x+y)}{1+sin(x+y)}$

Step-by-step explanation:

Given  y = cos (x +y) ...(i)

we will use formula

$\frac{d(cosx)}{dx} = - sinx$

Differentiating equation (i) with respective to 'x'

       $\frac{dy}{dx} = - sin ( x+y) X \frac{d}{dx} (x +y)$

      $\frac{dy}{dx} = - sin ( x+y) (1 + \frac{d y}{d x} )$

on simplification , we get

   $\frac{dy}{dx} = - sin ( x+y) - (sin(x+y) \frac{d y}{d x} )$

  $\frac{dy}{dx} + (sin(x+y) \frac{d y}{d x} ) = - sin (x +y)$

Taking common $\frac{dy}{dx}$  

$(1 + (sin(x+y)) \frac{d y}{d x} ) = - sin (x +y)$

                         $\frac{d y}{d x} = \frac{-sin(x+y)}{1+sin(x+y)}$