Derivative of \( \displaystyle 3 \sqrt{x^{2} + 4 x + 5} \)

Problem 2.1854 · hard

1. \[ \frac{d}{d x} 3 \sqrt{x^{2} + 4 x + 5} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 3 \frac{d}{d x} \sqrt{x^{2} + 4 x + 5} \]
   constant-multiple rewritePull the constant out of the derivative. Rewrite the square root as a fractional power.✓ Proved
3. \[ = \frac{3 \frac{d}{d x} \left(x^{2} + 4 x + 5\right)}{2 \sqrt{x^{2} + 4 x + 5}} \]
   chainApply the chain rule.✓ Proved
4. \[ = \frac{3 \left(2 x + 4\right)}{2 \sqrt{x^{2} + 4 x + 5}} \]
   derivativeDifferentiate the inner function.✓ Proved
5. \[ = \frac{3 \left(x + 2\right)}{\sqrt{x^{2} + 4 x + 5}} \]
   algebraFactor out a 2 from the inner derivative.✓ Proved
6. \[ = \frac{3 x + 6}{\sqrt{x^{2} + 4 x + 5}} \]
   simplify simplifySimplify the coefficients. Rewrite with a positive exponent in the denominator.✓ Proved