Derivative of \( \displaystyle - \frac{\sqrt{9 x^{2} - 18 x + 10}}{3} \)

Problem 2.1754 · hard

1. \[ \frac{d}{d x} \left(- \frac{\sqrt{9 x^{2} - 18 x + 10}}{3}\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = - \frac{\frac{d}{d x} \sqrt{9 x^{2} - 18 x + 10}}{3} \]
   constant rewritePull out the constant factor. Rewrite the square root as a fractional exponent.✓ Proved
3. \[ = - \frac{\frac{d}{d x} \left(9 x^{2} - 18 x + 10\right)}{6 \sqrt{9 x^{2} - 18 x + 10}} \]
   chain algebraApply the chain rule. Multiply the constants.✓ Proved
4. \[ = - \frac{18 x - 18}{6 \sqrt{9 x^{2} - 18 x + 10}} \]
   derivativeDifferentiate the inner polynomial.✓ Proved
5. \[ = - \frac{3 \left(x - 1\right)}{\sqrt{9 x^{2} - 18 x + 10}} \]
   algebraFactor out 18 from the polynomial derivative.✓ Proved
6. \[ = \frac{3 - 3 x}{\sqrt{9 x^{2} - 18 x + 10}} \]
   algebra simplifySimplify the coefficients. Rewrite with a positive exponent.✓ Proved