Find dy/dx if y = sin⁻¹(6x√(1-x²/25))

y = sin⁻¹(6x√(1-x²/25))
Taking sin on both sides, we get
sin(y) = 6x√(1-x²/25)
Differentiate both sides with respect to x,
cos(y)dy/dx = 6/5 * [ (√(1-x²/25)) - (x²/√(1-x²/25)) ]
√(1-sin²y) dy/dx = 6/5 * [ (√(1-x²/25)) - (x²/√(1-x²/25)) ]
√(1-(6x√(1-x²/25))²) dy/dx = 6/5 * [(1 - 2x²/25)/√(1-x²/25)]
dy/dx = 6/5 * [(1 - 2x²/25)/(√(1-x²/25)) * 1/√(1-(6x√(1-x²/25))²)]
dy/dx = 6/5 * [(25-2x²)/(25√(1-x²/25)) * 1/√(1-36x²(1-x²/25))]