Derivative of \( \displaystyle \frac{3 \sqrt{25 x^{2} - 30 x + 10}}{5} \)

Problem 2.1513 · hard

1. \[ \frac{d}{d x} \frac{3 \sqrt{25 x^{2} - 30 x + 10}}{5} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{3 \frac{d}{d x} \sqrt{25 x^{2} - 30 x + 10}}{5} \]
   constant-multiple rewritePull out the constant factor. Rewrite the square root as a fractional power.✓ Proved
3. \[ = \frac{3 \frac{d}{d x} \left(25 x^{2} - 30 x + 10\right)}{10 \sqrt{25 x^{2} - 30 x + 10}} \]
   chain algebraApply the chain rule. Simplify the constant coefficient.✓ Proved
4. \[ = \frac{3 \left(50 x - 30\right)}{10 \sqrt{25 x^{2} - 30 x + 10}} \]
   derivativeDifferentiate the inner polynomial.✓ Proved
5. \[ = \frac{3 \left(5 x - 3\right)}{\sqrt{25 x^{2} - 30 x + 10}} \]
   algebra algebraFactor out 10 from the polynomial. Cancel the 10 in the numerator and denominator.✓ Proved
6. \[ = \frac{15 x - 9}{\sqrt{25 x^{2} - 30 x + 10}} \]
   simplifyRewrite the negative exponent as a denominator.✓ Proved