Question

What is the derivative of y=tan(arcsin(x))?

Answer 1

Hello,

(tg(x))'=1/cos²(x)

(arcsin(x))'=1/√(1-x²)

cos²(arcsin(x))=1-sin²(arcsin(x))=1-x²



`(tg(arcsin(x)))'= (1)/(cos(arcsin(x)))^2) * (1)/(√(1-x^2)) \\ =(1)/(1-sin(arcsin(x))^2)* (1)/(√(1-x^2)) \\ = (1)/(1-x^2) * (1)/(√(1-x^2)) \\ \boxed{= (√(1-x^2))/(x^4-2x^2+1)}\\`