Derivative of \( \displaystyle 16 x^{3} - 36 x^{2} + 27 x \)

Problem 2.1760 · medium

1. \[ \frac{d}{d x} \left(16 x^{3} - 36 x^{2} + 27 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} 27 x - \frac{d}{d x} 36 x^{2} + \frac{d}{d x} 16 x^{3} \]
   sumApply the sum rule.✓ Proved
3. \[ = 27 \frac{d}{d x} x - 36 \frac{d}{d x} x^{2} + 16 \frac{d}{d x} x^{3} \]
   constant-multipleApply the constant multiple rule to each term.✓ Proved
4. \[ = 48 x^{2} - 72 x + 27 \]
   power algebraApply the power rule to each term. Simplify the coefficients.✓ Proved