Differentiate the following functions with respect to x: sin^-1{(sin x + cos x)/√2}, - 3π/4 < x < π/4

Question

Differentiate the following functions with respect to x:

sin^-1\(\Big\{\cfrac{sin\,\mathrm x +cos\,\mathrm x}{\sqrt2}\Big\},\) \(-\cfrac{3\pi}4\) < x < \(\cfrac{\pi}4\)

Answer 1

y = \(\Big\{\cfrac{sin\,\mathrm x +cos\,\mathrm x}{\sqrt2}\Big\}\)

Now