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

Question

Differentiate the following function with respect to x:

cos^-1\(\Big\{\frac{\mathrm x+\sqrt{1 - \mathrm x^2}}{\sqrt2}\Big\},\) -1 < x < 1

Answer 1

y = cos^-1\(\Big\{\frac{\mathrm x+\sqrt{1 - \mathrm x^2}}{\sqrt2}\Big\}\)

Let x = sinθ

Now

Now,