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

Problem 2.667 · medium

1. \[ \frac{d}{d x} 5 x \left(x - 6\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 5 \frac{d}{d x} x \left(x - 6\right) \]
   constant-multiplePull out the constant factor 5.✓ Proved
3. \[ = 5 x \frac{d}{d x} \left(x - 6\right) + 5 \left(x - 6\right) \frac{d}{d x} x \]
   productApply the product rule.✓ Proved
4. \[ = 5 x \frac{d}{d x} \left(x - 6\right) + 5 x - 30 \]
   derivativeDifferentiate the first part of the product.✓ Proved
5. \[ = 5 x \left(- \frac{d}{d x} 6 + \frac{d}{d x} x\right) + 5 x - 30 \]
   sumDifferentiate the second part of the product.✓ Proved
6. \[ = 10 x - 30 \]
   derivative algebra algebra simplifyDifferentiate the terms inside the parentheses. Simplify the expression inside the parentheses. Combine like terms. Distribute the 5 to get the final answer.✓ Proved