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

Problem 2.711 · medium

1. \[ \frac{d}{d x} 2 x \left(2 x + 1\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} 2 x + \frac{d}{d x} 4 x^{2} \]
   algebra algebraDistribute the term 2*x into the parentheses. Simplify the terms inside the derivatives.✓ Proved
3. \[ = 2 \frac{d}{d x} x + 4 \frac{d}{d x} x^{2} \]
   constant-multiplePull out the constant factors.✓ Proved
4. \[ = 8 x + 2 \]
   power algebraApply the power rule to each term. Multiply the constants.✓ Proved