Question

How do you implicitly differentiate `-1=sin(x+y)`?

Answer 1

`dy/dx= -1`

Explanation:

We apply the identity that if `sinx = y`, then `arcsiny = x`.

`arcsin(-1) = x + y`

The value of `arcsin(-1)`, or `270˚`, is just a constant, so the derivative will be `0`.

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

`0 = 1 + dy/dx`

`dy/dx= -1`

Hopefully this helps!