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How do you differentiate #sqrt(sin^2(1/x) # using the chain rule?

1 Answer

Jun 30, 2018

#f^'(x)=-1/(2 x^2*sqrt ((sin^2(1/x)))) * sin(2/x)#

Explanation:

#f(x)=sqrt(sin^2(1/x))= (sin^2(1/x))^(1/2)#

#f^'(x)=1/2(sin^2(1/x))^(-1/2)* 2 sin(1/x)* cos(1/x)* -1/x^2#

#f^'(x)=1/(2(sin^2(1/x))^(1/2))* sin(2/x)* -1/x^2#

#f^'(x)=-1/(2x^2*sqrt((sin^2(1/x)))) * sin(2/x)# [Ans]

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