Question

Find dy/dx using implicit differentiation
cos x + sin y = 1

Answer 1

Differentiate both sides with respect to x, using the chain rule for the sine term:

`\cos(x) + \sin(y) = 1`

`\implies -\sin(x) + \cos(y)(\mathrm dy)/(\mathrm dx) = 0`

Solve for dy/dx :

`-\sin(x) + \cos(y)(\mathrm dy)/(\mathrm dx) = 0 \\\\ \cos(y) (\mathrm dy)/(\mathrm dx) = \sin(x) \\\\ \boxed{(\mathrm dy)/(\mathrm dx) = (\sin(x))/(\cos(y))}`