What is the derivative of $f(x) = tan(x)cos(x)$ ?

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Answer 1 · 2015-11-02T15:12:15

$f'(x) = cosx$

This is a trick or trap question.

The long and tedious way to this in by the product rule, then simplify.

The quicker way is to observe that

$f(x) = tanx cosx = sinx/cosx cosx = sinx$ .

So, $f'(x) = cosx$ .

What is the derivative of f(x) = tan(x)cos(x)f(x) = tan(x)cos(x)?