Question

How do you find dy/dx for the function `y=sin(2x+4y)`?

Answer 1

You have an Implicit Function in which `y` is function of `x` so you have to derive it as well.
You get:
`dy/dx=[cos(2x+4y)]*[2+4dy/dx]`
where you use the Chain Rule on the `sin` function.

`dy/dx=2cos(2x+4y)+4cos(2x+4y)dy/dx`
Collecting `dy/dx`:
`dy/dx[1-4cos(2x+4y)]=2cos(2x+4y)`
`dy/dx=(2cos(2x+4y))/(1-4cos(2x+4y))`

Hope it helps