Question

What is the derivative of `sqrt(x^2+1)`?

Answer 1

`x/sqrt(x^2+1)`

Explanation:

Using the chain rule
If a function `f(x)=[g(x)]^n`

Then `f'(x)=n[g(x)]^(n-1)cdot g'(x)`

Given `g(x)=(x^2+1) and n=1/2`
We see that `g'(x)=2x`
`:. text{derivative of }(x^2+1)^(1/2)=1/2[x^2+1]^(1/2-1)cdot 2x`
`=1/ cancel2[x^2+1]^(-1/2)cdot cancel2 x`
or `=x[x^2+1]^(-1/2)`
or `=x/sqrt(x^2+1)`