How do you differentiate

Question

arcsin(5x)?

Answer 1

The derivative of sin^-1 x = 1/√(1 - x²)

For sin^-1 (5x),

let u = 5x

du/dx = 5

Then d/dx sin^-1 (u) = [1/√(1 - u²)] * du/dx

= 5 / √[1 - (5x)² ]

Therefore d/dx sin^-1 (5x) =  5 / √[1 - (5x)² ]