Question

Question #f6a18

Answer 1

`d/dx(ln sqrt(x^2+1))=x/(x^2+1)`

Explanation:

By rewriting a square-root as a 1/2-power and `ln x^r=r ln x`,

`lnsqrt(x^2+1)=ln(x^2+1)^(1/2)=1/2 ln(x^2+1)`

By Log Rule & Chain Rule,

`f'(x)=1/cancel(2)cdot1/(x^2+1)cdot cancel(2)x=x/(x^2+1)`

I hope that this was clear.