Differentiation of tan - 1 ⁡ x 1 - x 2 with respect to sin - 1 ⁡ ( 3 x - 4 x 3 ) is .....

Step-by-step solution

L e t x = s i n θ then f θ = tan - 1 ⁡ sin ⁡ θ 1 - sin 2 ⁡ θ = θ and g θ = sin - 1 ⁡ ( 3 s i n θ - 4 sin 3 ⁡ θ ) = sin - 1 ⁡ ( sin ⁡ 3 θ ) = 3 θ Differentiating f w.r.t to g ⟹ d f θ d θ d g θ d θ = 1 3