Question

How do you implicitly differentiate `sin x + cos y = sin x cos y`?

Answer 1

`dy/dx = (cosx - cosxcosy)/(siny - sinxsiny)`

Explanation:

Use implicit differentiation and the rules that `d/dx(cosx) = -sinx` and `d/dx(sinx) = cosx`.

`cosx - siny(dy/dx) = cosxcosy + (sinx xx -siny(dy/dx))`

`cosx- siny(dy/dx) = cosxcosy - sinxsiny(dy/dx)`

`cosx - cosxcosy = siny(dy/dx) - sinxsiny(dy/dx)`

`cosx - cosxcosy = dy/dx(siny - sinxsiny)`

`(cosx - cosxcosy)/(siny - sinxsiny) = dy/dx`