`cos(x + y) = x` Find `dy/dx` by implicit differentiation.

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Chapter 2, Review - Problem 82 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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Note:- If y = cos(x) ; then dy/dx = -sin(x)

Now, 

`cos(x+y) = x`

`or, -sin(x+y)*{1 + (dy/dx)} = 1`

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

`or, 1+(dy/dx) = -cosec(x+y)`

`or, dy/dx = -1 - cosec(x+y)`

`or, dy/dx = -{1+cosec(x+y)}`

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