Derivative of \( \displaystyle 20 x^{3} - 90 x^{2} + 135 x \)

Problem 2.1766 · medium

1. \[ \frac{d}{d x} \left(20 x^{3} - 90 x^{2} + 135 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} 135 x - \frac{d}{d x} 90 x^{2} + \frac{d}{d x} 20 x^{3} \]
   sumApply the sum rule.✓ Proved
3. \[ = 135 \frac{d}{d x} x - 90 \frac{d}{d x} x^{2} + 20 \frac{d}{d x} x^{3} \]
   constant-multipleFactor out the constants.✓ Proved
4. \[ = 60 x^{2} - 180 x + 135 \]
   power algebraApply the power rule to each term. Multiply the coefficients.✓ Proved