Question

Differentiate the function with respect to x: cos^-1{(cos x + sin x)/√2}, -π/4 < x < π/4

Answer 1

Suppose y = cos^-1{(cos x + sin x)/√2}

As considering the limits,

-π/4 < x < π/4

-π/2 < x - π/4 < 0

Then 

y = -x + (π/4)

On differentiating with respect to x

dy/dx = -1