Question

How do you find the derivative of `sqrt(x^2+1)`?

Answer 1

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

This is a power and the chain rule. (A combination sometimes called "The General Power Rule: `d/(dx)((g(x))^r)=r(g(x))^(r-1) g'(x)`)

Because the square root appears so often, I encourage students to memorize:

`d/(dx)sqrtx = 1/(2sqrtx)`

For the function asked about:

`f'(x) = 1/(2sqrt(x^2+1)) * 2x = 1/(sqrt(x^2+1))`