Question

Differentiate the following functions w.r.t. x:

(i) sin^–1((3sinx + 4cos x)/5)

(ii) If y = tan^–1((1 – cosx)/sinx), find dy/dx

(iii) If y = tan^–1 (cos x/(1 – sin x)), find dy/dx

Answer 1

(i) Given y = sin^–1((3sinx + 4cosx)/5)

⇒ y = sin^–1(3/5sinx + 4/5cosx)

⇒ y = sin^–1(cosa sin x + sina cosx)

⇒ y = sin^–1(sin(x + a)) = (x + a)

⇒ dy/dx = 1, where a = tan^–1(4/3)