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

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Answer 1 · 2016-02-15T23:09:22

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

We can use the chain rule to create a rule for differentiating a cosine function:

Since $d/dx(cos(x))=-sin(x)$ , we know that $d/dx(cos(u))=-sin(u)*u'$ .

Applying this to $cos(tan(x))$ , where $u=tan(x)$ , we see that

$d/dx(cos(tan(x)))=-sin(tan(x))*d/dx(tan(x))$

It is helpful to know that $d/dx(tan(x))=sec^2(x)$ . Hence

$d/dx(cos(tan(x)))=-sin(tan(x))sec^2(x)$

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