What is the derivative of #(sinx+cosx)^2 +(sinx-cosx)^2#?

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Answer 1 · 2016-08-11T16:34:22

#0#

#f(x) = (sinx+cosx)^2 +(sinx-cosx)^2 = 2# so
#(df)/(dx) = 0#

Answer 2 · 2016-08-11T16:36:42

The function is constant so the derivative is #0#

#(sinx+cosx)^2+(sinx-cosx)^2 = (sin^2x+2sinxcosx+cos^2x)+ (sin^2x-2sinxcosx+cos^2x)#

# = 1+2sinxcosx + 1-2sinxcosx = 2#

#d/dx(2) = 0#