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What is the derivative of #cos( sin( x ))#?

1 Answer

Oct 20, 2016

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

Explanation:

#d/(dx)cos(sin(x))#

Using chain rule, #(dy)/(dx)=(dy)/(du)*(du)/(dx)#, let #u=sin(x)#

#(dy)/(du)=d/(du)cosu=-sinu=-sin(sin(x))#

#(du)/(dx)=d/(dx)sin(x)=cos(x)#

#:.(dy)/(dx)=-sin(sin(x))*cos(x)=-sin(sin(x))cos(x)#

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