Derivative of \( \displaystyle 3 x^{2} + 2 x \)

Problem 2.2011 · medium

1. \[ \frac{d}{d x} \left(3 x^{2} + 2 x\right) \]
   sumStart with the derivative of the entire function.✓ Proved
2. \[ = \frac{d}{d x} 2 x + \frac{d}{d x} 3 x^{2} \]
   sumApply the sum rule to differentiate each term separately.✓ Proved
3. \[ = \frac{d}{d x} 2 x + 3 \frac{d}{d x} x^{2} \]
   constant-multiplePull the constant 3 out of the first derivative.✓ Proved
4. \[ = 2 \frac{d}{d x} x + 3 \frac{d}{d x} x^{2} \]
   constant-multiplePull the constant 2 out of the second derivative.✓ Proved
5. \[ = 6 x + 2 \]
   power algebraApply the power rule to both terms. Multiply the constants through the parentheses.✓ Proved