Question

The derivative of `sqrt(x^2 + 1)` is

Options

• `x/sqrt(x^2 - 1)`

• `x/(2sqrt(x^2 - 1))`

• `(2x)/sqrt(x^2 - 1)`

• `x/sqrt(x^2 + 1)`

Answer 1

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

Explanation:

Let y = `sqrt(x^2 + 1)`

∴ `"dy"/"dx" = 1/(2sqrt(x^2 + 1)) "d"/"dx" (x^2 + 1)`

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

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