Question

Find d/dx of sin inverse (2x/4x^2)?

Answer 1

d / dx[sin^-11(2x / 4x²) = d /dx[sin^-11( 1 / 2x)

Let 1 / 2x = t

Difereciate with respective x

1 / 2(-1 / x²) = dt

                                = d /dx[sin^-11(t)

                                = 1 / √(1 - t²) dt

                                =  1 / √(1 - (1 / 2x)²) 1 / 2( -1 / x²)

                                = 1 / √(1 - 1 / 4x²) × - 1 / 2x²

                                = 1 / [√(4x² - 1) / 2x] (- 1 / 2x²)

                                = [2x / √(4x² - 1)][ -1 / 2x²]

Simplify

                                = -1 / x√(4x² - 1) .