Derivative of \( \displaystyle 6 x \left(x - 2\right) \)

Problem 2.145 · easy

1. \[ \frac{d}{d x} 6 x \left(x - 2\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 6 \frac{d}{d x} x \left(x - 2\right) \]
   constant-multiplePull out the constant factor 6.✓ Proved
3. \[ = 6 x \frac{d}{d x} \left(x - 2\right) + 6 \left(x - 2\right) \frac{d}{d x} x \]
   productApply the product rule to x*(x - 2).✓ Proved
4. \[ = 6 x \frac{d}{d x} \left(x - 2\right) + 6 x - 12 \]
   derivativeDifferentiate the first part of the product.✓ Proved
5. \[ = 6 x \left(- \frac{d}{d x} 2 + \frac{d}{d x} x\right) + 6 x - 12 \]
   sumDifferentiate the second part of the product.✓ Proved
6. \[ = 12 x - 12 \]
   derivative algebra algebra algebraEvaluate the derivatives of x and 2. Simplify the expression inside the parentheses. Combine like terms. Distribute the 6 to get the final answer.✓ Proved