Derivative of \( \displaystyle 2 x \left(- 2 x - 1\right) \)

Problem 2.693 · medium

1. \[ \frac{d}{d x} 2 x \left(- 2 x - 1\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 2 \frac{d}{d x} x \left(- 2 x - 1\right) \]
   constant-multiplePull out the constant factor 2.✓ Proved
3. \[ = 2 x \frac{d}{d x} \left(- 2 x - 1\right) + 2 \left(- 2 x - 1\right) \frac{d}{d x} x \]
   productApply the product rule.✓ Proved
4. \[ = 2 x \frac{d}{d x} \left(- 2 x - 1\right) - 4 x - 2 \]
   derivativeDifferentiate the first part of the product.✓ Proved
5. \[ = - 8 x - 2 \]
   derivative algebra simplify algebraDifferentiate the second part of the product. Distribute the x into the derivative term. Combine like terms inside the parentheses. Distribute the 2 to get the final simplified form.✓ Proved