Derivative of \( \displaystyle 10 x \left(2 x - 3\right) \)

Problem 2.1377 · medium

1. \[ \frac{d}{d x} 10 x \left(2 x - 3\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(20 x^{2} - 30 x\right) \]
   algebra algebraDistribute the terms inside the parentheses. Simplify the coefficients.✓ Proved
3. \[ = - \frac{d}{d x} 30 x + \frac{d}{d x} 20 x^{2} \]
   sumApply the difference rule.✓ Proved
4. \[ = - 30 \frac{d}{d x} x + 20 \frac{d}{d x} x^{2} \]
   constant-multipleFactor out the constants.✓ Proved
5. \[ = 40 x - 30 \]
   power algebraDifferentiate the power terms. Multiply the remaining terms.✓ Proved