Derivative of \( \displaystyle 4 x \left(x + 1\right) \)

Problem 2.78 · easy

1. \[ \frac{d}{d x} 4 x \left(x + 1\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 4 \frac{d}{d x} x \left(x + 1\right) \]
   constant-multiplePull out the constant factor 4.✓ Proved
3. \[ = 4 x \frac{d}{d x} \left(x + 1\right) + 4 \left(x + 1\right) \frac{d}{d x} x \]
   productApply the product rule to x*(x + 1).✓ Proved
4. \[ = 4 x \frac{d}{d x} \left(x + 1\right) + 4 x + 4 \]
   derivative algebraDifferentiate x and (x + 1). Simplify the expression inside the parentheses.✓ Proved
5. \[ = 4 x \left(\frac{d}{d x} 1 + \frac{d}{d x} x\right) + 4 x + 4 \]
   sumApply the sum rule to the derivative of (x + 1).✓ Proved
6. \[ = 8 x + 4 \]
   derivative algebra algebra algebraDifferentiate x and the constant 1. Simplify the expression inside the parentheses. Combine like terms. Distribute the 4.✓ Proved