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

Problem 2.92 · easy

1. \[ \frac{d}{d x} 3 x \left(x - 2\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(3 x^{2} - 6 x\right) \]
   algebraExpand the expression using the distributive property.✓ Proved
3. \[ = - 6 \frac{d}{d x} x + 3 \frac{d}{d x} x^{2} \]
   sumApply the sum rule for differentiation.✓ Proved
4. \[ = 6 x - 6 \]
   power algebraDifferentiate each term using the power rule. Simplify the resulting expression.✓ Proved