Question

If `y=2x+tanx`, find `y'''` third derivative of `y`?

Answer 1

`y'''=4sec^2xtan^2x+2sec^4x`

Explanation:

As `y=2x+tanx`

`y'=2xx1+sec^2x=2+sec^2x`

• differentiating both separately

`y''=2secx xx secx tanx=2sec^2xtanx`

• differential of constant term is `0` and using chain rule.

`y'''=2(2sec^2xtanx)tanx+2sec^2x(sec^2x)`

`=4sec^2xtan^2x+2sec^4x`

• using product rule