Derivative of \( \displaystyle x \left(6 - 5 x\right) \)

Problem 2.1105 · medium

1. \[ \frac{d}{d x} x \left(6 - 5 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(- 5 x^{2} + 6 x\right) \]
   algebraDistribute x into the parentheses.✓ Proved
3. \[ = \frac{d}{d x} 6 x - \frac{d}{d x} 5 x^{2} \]
   sumApply the difference rule.✓ Proved
4. \[ = 6 \frac{d}{d x} x - 5 \frac{d}{d x} x^{2} \]
   constantPull out the constant factor.✓ Proved
5. \[ = 6 - 5 \frac{d}{d x} x^{2} \]
   derivative simplifyDifferentiate the first term. Simplify the expression.✓ Proved
6. \[ = 6 - 10 x \]
   power algebraApply the power rule to x**2. Multiply the constants.✓ Proved