Differentiate √(1+Sin x) +√(1-x^2)÷(1+x^2)

Question

Need full solution

Answer 1

Let A = (1/2)(1+x²)[cos x (1 + sin x)^-1/2 + 2x(1-x²)^-1/2]

Let B = 2x[(1 + sin x)^1/2 +  (1 - x²)^1/2]

 

The derivative sought then is (A - B)/[(1 + x²)²

 

Recently one of my classes taught me this little jngle:

 

Downsie d upsie - upsie d downsie divided by downsie squared