Derivative of \( \displaystyle \sqrt{x^{2} + 1} \)

Problem 2.47 · easy

1. \[ \frac{d}{d x} \sqrt{x^{2} + 1} \]
   derivative rewriteStart with the derivative of the function. Rewrite the square root as a fractional exponent.✓ Proved
2. \[ = \frac{\frac{d}{d x} \left(x^{2} + 1\right)}{2 \sqrt{x^{2} + 1}} \]
   chainApply the chain rule.✓ Proved
3. \[ = \frac{x}{\sqrt{x^{2} + 1}} \]
   derivative algebra simplifyDifferentiate the inner function. Simplify the expression by canceling the 2. Rewrite with a positive exponent.✓ Proved