Derivative of \( \displaystyle 80 x^{3} + 120 x^{2} + 60 x \)

Problem 2.1757 · medium

1. \[ \frac{d}{d x} \left(80 x^{3} + 120 x^{2} + 60 x\right) \]
   sumStart with the derivative of the entire function.✓ Proved
2. \[ = \frac{d}{d x} 60 x + \frac{d}{d x} 120 x^{2} + \frac{d}{d x} 80 x^{3} \]
   sumApply the sum rule to differentiate each term separately.✓ Proved
3. \[ = 60 \frac{d}{d x} x + 120 \frac{d}{d x} x^{2} + 80 \frac{d}{d x} x^{3} \]
   constant-multiplePull out the constant coefficients.✓ Proved
4. \[ = 240 x^{2} + 240 x + 60 \]
   power algebraApply the power rule to each term. Multiply the constants.✓ Proved