If y = sin-1(3x - 4x3) then dy/dx = ?A. 3/√1-x2B. -4/√1-x2C. 3/�

1.	If y = sin-1(3x - 4x3) then dy/dx = ?A. 3/√1-x2B. -4/√1-x2C. 3/√1+x2D. none of these
Answer» Answer is: 3/√1-x² Given that y = sin^-1(3x - 4x³) Let x = sin θ ⇒ θ = sin^-1x Then, y = sin^-1(3sinθ - 4sin³θ) Using sin3θ = 3sinθ - 4sin 3θ, we get y = sin^-1(sin3θ) = 3θ = 3sin^-1x Differentiating with respect to x, we get dy/dx = 3/√1-x²

If y = sin-1(3x - 4x3) then dy/dx = ?A. 3/√1-x2B. -4/√1-x2C. 3/√1+x2D. none of these

Answer»

Answer is: 3/√1-x²

Given that y = sin^-1(3x - 4x³)

Let x = sin θ

⇒ θ = sin^-1x

Then, y = sin^-1(3sinθ - 4sin³θ)

Using sin3θ = 3sinθ - 4sin 3θ, we get

y = sin^-1(sin3θ) = 3θ = 3sin^-1x

Differentiating with respect to x, we get

dy/dx = 3/√1-x²