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

Question

13203 views around the world

You can reuse this answer
Creative Commons License

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 $0$

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

$= 1+2sinxcosx + 1-2sinxcosx = 2$

$d/dx(2) = 0$

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