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

Answer 1

Luke Alvarez

#-(4sin(1/x^2)cos(1/x^2))/x^3#

Writing your function in the form

#(sin(1/x^2))^2# and we get by the power and the chain rule

#2sin(1/x^2)cos(1/x^2)*2(1/x)*(-1/x^2)# this is

#-(4sin(1/x^2)*cos(1/x^2))/x^3#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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