Derivative of \( \displaystyle 50 x^{3} + 60 x^{2} + 24 x \)

Problem 2.1933 · medium

1. \[ \frac{d}{d x} \left(50 x^{3} + 60 x^{2} + 24 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} 24 x + \frac{d}{d x} 60 x^{2} + \frac{d}{d x} 50 x^{3} \]
   sumApply the sum rule.✓ Proved
3. \[ = 2 \frac{d}{d x} 12 x + 60 \frac{d}{d x} x^{2} + 50 \frac{d}{d x} x^{3} \]
   constant-multiplePull out the constants.✓ Proved
4. \[ = 24 \frac{d}{d x} x + 60 \frac{d}{d x} x^{2} + 50 \frac{d}{d x} x^{3} \]
   constant-multipleSimplify the constant terms.✓ Proved
5. \[ = 150 x^{2} + 120 x + 24 \]
   power algebraApply the power rule to each term. Multiply the constants.✓ Proved