1 answer
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d((sinx) ^2-(cosx) ^2)/dx
= 2sinxcosx - 2cosx(-sinx)
= 4 sinxcosx
I don't know how your calculator got -4sinxcosx.
Your answer might also expect you to go a bit further.
recall that sin 2A = 2 sinAcosA
so 4 sinxcosx = 2(2sinxcosx) = 2sin2x