Question

How do you find the differential `dy` of the function `y=2x-cot^2x`?

Answer 1

For `y = f(x)`, the differential of `y` is `dy = f'(x) dx`

Explanation:

In this question we have `f'(x) = 2x-cot^2x`

so

`f'(x) = 2-2cotx * d/dx(cotx) = 2-2cotx*(-csc^2x)`

`f'(x) = 2+2cotxcsc^2x`

And so, `dy = (2+2cotxcsc^2x) dx`