Differentiate the following functions with respect to x:
Now
Using cos2θ = 2cos2θ – 1
y = cos–1(cosθ)
Considering the limits,
–1< x < 1
–1< cos2θ < 1
0 < 2θ < π
Now, y = cos–1(cosθ)
y = θ
Differentiating w.r.t x, we get