Question

How do you differentiate `f(x)=sec^2x-tan^2x`?

Answer 1

See below

Explanation:

`(df)/dx=2secx(dsecx)/dx-2tanx(dtanx)/dx=2secxtanxsecx-2tanxsec^2x=2sec^2xtanx-2sec^2xtanx=0`

This obvious result is the consecuence of the fact

`sec^2x-tan^2x=1/(cos^x)-sin^2x/cos^2x=(1-sin^2x)/cos^2x=cos^2x/cos^2x=1`

Therefore `f(x)` is a constant function for every `x`. For this reason his derivative is zero