Differentiate the following functions with respect to x:

Question

Philoid · Accepted Answer

Let x = a sinθ

Now

Using sin²θ + cos²θ = 1

y = tan^–1(tanθ)

Considering the limits,

–a < x < a

–a < asin θ < a

–1 < sin θ < 1

Now, y = tan^–1(tanθ)

y = θ

Differentiating w.r.t x, we get