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

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This obvious result is the consecuence of the fact

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To differentiate ( f(x) = \sec^2(x) - \tan^2(x) ), you can use the following steps:

- Identify the individual functions: ( \sec(x) ) and ( \tan(x) ).
- Apply the chain rule to differentiate each function.
- Substitute the derivatives back into the original expression and simplify.

Differentiate ( \sec(x) ) and ( \tan(x) ):

( \frac{d}{dx}(\sec(x)) = \sec(x) \tan(x) ) ( \frac{d}{dx}(\tan(x)) = \sec^2(x) )

Substitute derivatives back into the original expression:

( f'(x) = \sec(x) \tan(x) - \sec^2(x) )

Simplify by factoring out ( \sec(x) ):

( f'(x) = \sec(x)(\tan(x) - \sec(x)) )

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