Derivative of \( \displaystyle x \left(- 3 x - 2\right) \)

Problem 2.1344 · medium

1. \[ \frac{d}{d x} x \left(- 3 x - 2\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = x \frac{d}{d x} \left(- 3 x - 2\right) + \left(- 3 x - 2\right) \frac{d}{d x} x \]
   productApply the product rule.✓ Proved
3. \[ = x \frac{d}{d x} \left(- 3 x - 2\right) - 3 x - 2 \]
   derivativeDifferentiate the first part of the product.✓ Proved
4. \[ = x \frac{d}{d x} \left(-2\right) + x \frac{d}{d x} \left(- 3 x\right) - 3 x - 2 \]
   sumApply the sum rule to the second part.✓ Proved
5. \[ = - 3 x \frac{d}{d x} x - 3 x - 2 \]
   constantDifferentiate the terms in the sum.✓ Proved
6. \[ = - 6 x - 2 \]
   derivative algebra simplifyDifferentiate the remaining x terms. Simplify the expression. Combine like terms.✓ Proved