Question

What is the derivative of `y=sec^2 x + tan^2 x`?

Answer 1

`f'(x)=2sec^2(x)tan(x)+2tan(x)*(1+tan^2(x))`

Explanation:

Note that

`(sec(x))'=sec(x)tan(x)`
`(tan(x))'=1+tan^2(x)`

Answer 2

Shown below...

Explanation:

Another way of thinking about it:

`1 + tan^2 x = sec^2 x`

`=>1 + tan^2x + tan^2 x = sec^2 x + tan^2 x`

`=> 1 + 2tan^2 x = sec^2 x + tan^2 x`

`=> d/dx ( 1 + 2 tan^2 x )`

Use `d/dx tanx = sec^2 x`

Use chain rule:

`= 2*2tanx * d/dx tanx`

`= 4tanx sec^2x`