Question

How do you differentiate `tanx+tany=1`?

Answer 1

`dy/dx = - sec^2x/sec^2y`

Explanation:

When we differentiate `y` wrt `x` we get `dy/dx`.

However, we cannot differentiate a non implicit function of `y` wrt `x`. But if we apply the chain rule we can differentiate a function of `y` wrt `y` but we must also multiply the result by `dy/dx`.

When this is done in situ it is known as implicit differentiation.

We have:

`tanx + tany = 1`

Differentiate wrt `x`:

`sec^2x + sec^2ydy/dx = 0`
`:. sec^2ydy/dx = - sec^2x`
`:. dy/dx = - sec^2x/sec^2y`