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

Problem 2.16 · medium

1. \[ \frac{d}{d x} \left(- \frac{\sqrt{16 x^{2} + 1}}{4}\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = - \frac{\frac{d}{d x} \sqrt{16 x^{2} + 1}}{4} \]
   constant rewritePull out the constant factor. 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. \[ = - \frac{4 x}{\sqrt{16 x^{2} + 1}} \]
   derivative algebra simplify rewriteDifferentiate the inner function. Multiply the terms. Simplify the coefficient. Rewrite the negative exponent as a fraction.✓ Proved