What is the derivative of x Times Square root of xx plus 1?

Answer 1

F(x)=x*Sqrt(x^2+1)

let f(x)=x

let g(x)=Sqrt(x^2+1)

F'(x)=f'(x)*g(x)+f(x)*g'(x)

f'(x)=1

Use chain rule:

g'(x)=(x)*(x^2+1)^(-1/2)

F'(x)=Sqrt(x^2+1)+(x^2)/Sqrt(x^2+1)