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)#