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

Problem 2.1752 · hard

1. \[ \frac{d}{d x} \frac{5 \sqrt{4 x^{2} - 4 x + 2}}{2} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{5 \frac{d}{d x} \sqrt{4 x^{2} - 4 x + 2}}{2} \]
   constant-multiple rewritePull out the constant factor. Rewrite the square root as a power.✓ Proved
3. \[ = \frac{5 \frac{d}{d x} \left(4 x^{2} - 4 x + 2\right)}{4 \sqrt{4 x^{2} - 4 x + 2}} \]
   chain algebraApply the chain rule. Simplify the constant coefficients.✓ Proved
4. \[ = \frac{5 \left(8 x - 4\right)}{4 \sqrt{4 x^{2} - 4 x + 2}} \]
   derivativeDifferentiate the inner polynomial.✓ Proved
5. \[ = \frac{10 x - 5}{\sqrt{4 x^{2} - 4 x + 2}} \]
   algebra simplifyMove the negative exponent to the denominator. Simplify the expression by factoring out 4 from the numerator and denominator.✓ Proved