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

1 Answer
Nov 24, 2016

dy/dx= -1dydx=1

Explanation:

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

arcsin(-1) = x + yarcsin(1)=x+y

The value of arcsin(-1)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!