Derivative of \( \displaystyle 2 x \left(5 x - 6\right) \)

Problem 2.1410 · medium

1. \[ \frac{d}{d x} 2 x \left(5 x - 6\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(10 x^{2} - 12 x\right) \]
   algebra algebraDistribute the terms inside the parentheses. Simplify the coefficients.✓ Proved
3. \[ = - \frac{d}{d x} 12 x + \frac{d}{d x} 10 x^{2} \]
   sumApply the difference rule.✓ Proved
4. \[ = - 12 \frac{d}{d x} x + 10 \frac{d}{d x} x^{2} \]
   constant-multipleFactor out the constants.✓ Proved
5. \[ = 20 x - 12 \]
   power algebraDifferentiate the power terms. Multiply the remaining terms.✓ Proved