Question

Differentiate:
y=sqrt(1-x^2)*sin^-1x

Answer 1

y=√(1-x²)*arcsin(x)

Is a product, so you have to use the product rule.

xy=x' *y+ y' * x

Following this back to your function.

y=√(1-x²)*arcsin(x)


y'=(-x/√(1-x²))*arcsin(x)+1/√(1-x²)*√(1-x²))

Simplificating

y'=(-x/√(1-x²))*arcsin(x)+1)

Answer 2

Thanks