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:

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

$\implies -\sin(x) + \cos(y)\dfrac{\mathrm dy}{\mathrm dx} = 0$

Solve for dy/dx :

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