How do you differentiate $f (x) = \frac{1 + {tan}^{2} x}{sec x}$ $f(x)=(1+tan^2x)/secx$ ?

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Answer 1 · 2016-10-31T20:30:58

$f (x) = \frac{1 + {tan}^{2} x}{sec x}$ $f(x)=(1+tan^2x)/secx$

$= \frac{{sec}^{2} x}{sec x}$ $=sec^2x/secx$

$= sec x$ $=secx$

Which means that:

$f' (x) = sec x tan x$ $f'(x)=secxtanx$

Watch this video to find out how to differentiate secx:

You may also need to see some handy **trigonometric rules ** .

How do you differentiate f(x)=1+tan2xsecxf(x)=(1+tan^2x)/secx?