how do i find the derivative of........ (sinx) ^2-(cosx) ^2 i put it into my t-89 and got -4sinxcosx butthats not a multiple choice. can someone tel me how to do this by hand?

Answer 1

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