Derivative of \( \displaystyle \frac{\sqrt{16 x^{2} + 1}}{4} \)

Problem 2.242 · medium

1. \[ \frac{d}{d x} \frac{\sqrt{16 x^{2} + 1}}{4} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{\frac{d}{d x} \sqrt{16 x^{2} + 1}}{4} \]
   constant-multiple rewritePull out the constant factor 1/4. Rewrite the square root as a fractional power.✓ Proved
3. \[ = \frac{\frac{d}{d x} \left(16 x^{2} + 1\right)}{8 \sqrt{16 x^{2} + 1}} \]
   chain algebraApply the chain rule. Multiply the constants.✓ Proved
4. \[ = \frac{4 x}{\sqrt{16 x^{2} + 1}} \]
   power algebra simplifyDifferentiate the inner function 16*x**2 + 1. Combine the terms into a single fraction. Simplify the fraction by dividing 32 by 8.✓ Proved