Differentiate

Given expression :

√1+x/a - √1-x/a√1+x/a + √1-x/a

Putting cos(2θ) = x/a and making the substitutions,

1+cos(2θ) = 2cos²(θ) and 1-cos(2θ) = 2sin²(θ)

We get the expression to be:

cos(θ)-sin(θ)cos(θ)+sin(θ) = tan(π/4 - θ)

dθ/dx = d(1/2 * cos^-1x/a)dx = 12√a²-x²

Therefore dtan(Ï€/4 - θ)/dx = -sec²(Ï€/4 - 1/2*cos^-1x/a)2√a²-x²