Derivative of \( \displaystyle \frac{5 \sqrt{4 x^{2} + 1}}{2} \)

Problem 2.295 · medium

1. \[ \frac{d}{d x} \frac{5 \sqrt{4 x^{2} + 1}}{2} \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{5 \frac{d}{d x} \sqrt{4 x^{2} + 1}}{2} \]
   constant-multiple rewritePull out the constant factor. Rewrite the square root as a fractional exponent.✓ Proved
3. \[ = \frac{5 \frac{d}{d x} \left(4 x^{2} + 1\right)}{4 \sqrt{4 x^{2} + 1}} \]
   chain algebraApply the chain rule. Multiply the constants.✓ Proved
4. \[ = \frac{10 x}{\sqrt{4 x^{2} + 1}} \]
   power algebra simplify rewriteDifferentiate the inner function. Rearrange the terms. Simplify the expression. Convert the negative exponent back to a square root in the denominator.✓ Proved