What is the derivative of $cos(x^2)$ ?

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Answer 1 · 2016-03-11T18:03:34

$d/(dx)cos(x^2) =-2xsin(x^2)$

Let's use the chain rule

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

In other words:

$d/(dx)cos(x^2) = (d)/(du)cos(u) * (du)/(dx)$

where

$u=x^2$

doing each part individually:

$(d)/(du)cos(u)=-sin(u)$

and

$(du)/(dx)=d/(dx)x^2 = 2x$

putting this back together we get

$d/(dx)cos(x^2) =-2xsin(x^2)$

What is the derivative of cos(x^2)cos(x^2)?