How do you differentiate # f(x) = cos( sin( x ))#?

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Answer 1 · 2016-05-28T20:24:19

#=>(dy)/(dx)=-cos(x)sin(sin(x))#

Let #u= sin(x)#

Then #(du)/dx= cos(x)#

'..............................

Let #y=cos(u)#

Then #(dy)/(du)=-sin(u)#

'..............................................
But #(dy)/(dx)=(du)/(dx)xx(dy)/(du)#

#=>(dy)/(dx)=cos(x)xx(-sin(u))#

#=>(dy)/(dx)=-cos(x)sin(sin(x))#