Differentiate the following functions with respect to x:
Let x = a sinθ
Now
Using sin2θ + cos2θ = 1
Using 2cos2θ = 1 + cosθ and 2sinθ cosθ = sin2θ
Considering the limits,
–a < x < a
–1 < sin θ < 1
Now,
Differentiating w.r.t x, we get