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

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Answer 1 · 2016-06-23T00:06:36

$- sin (tan(x)) * sec^2 x$

$y = cos (tan x)$

$= cos (p), \qquad p = tan(x)$

so you chain rule it!

$dy/(dp) = - sin (p)$

$(dp)/dx = sec^2 x$

$dy/dx = dy/(dp) * (dp)/dx$

$= - sin (p) * sec^2 x$

$= - sin (tan(x)) * sec^2 x$

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