Question

y=x乘以根号下1+x^2 +arcsinx 的导数怎么求

Answer 1

y=x*(1+x²)^(1/2)+arcsinx

=(1+x²)^(1/2)+x*(1/2)(2x)*(1+x²)^(-1/2)+(1-x²)^(-1/2)

=(1+x²)^(1/2)+x²*(1+x²)^(-1/2)+(1-x²)^(-1/2)

=√(1+x²)+x²/√(1+x²)+1/√(1-x²)

=(1+2x²)/√(1+x²)+1/√(1-x²)