Question

How do you differentiate `ysinx=y`?

Answer 1

You can use the product rule, like the usual. Just remember that the derivative of y with respect to x in `(df)/(dx)` is `(dy)/(dx)`.

With `f(x): ysinx = y`,

`(df)/(dx)[ysinx = y] = ycosx + sinx((dy)/(dx)) = (dy)/(dx)`

`(dy)/(dx)[1-sinx] = ycosx`

`(dy)/(dx) = (ycosx)/(1-sinx)`

If you check Wolfram Alpha, you'll see this, just multiplied by `-1`.