Derivative of \( \displaystyle 3 x \ln{\left(x \right)} - 3 x \)

Problem 2.1937 · hard Beautiful

1. \[ \frac{d}{d x} \left(3 x \ln{\left(x \right)} - 3 x\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = - \frac{d}{d x} 3 x + \frac{d}{d x} 3 x \ln{\left(x \right)} \]
   sumApply the sum rule.✓ Proved
3. \[ = - \frac{d}{d x} 3 x + 3 \frac{d}{d x} x \ln{\left(x \right)} \]
   constant-multipleFactor out the constant 3.✓ Proved
4. \[ = 3 x \frac{d}{d x} \ln{\left(x \right)} + 3 \ln{\left(x \right)} \frac{d}{d x} x - \frac{d}{d x} 3 x \]
   productApply the product rule to the first term.✓ Proved
5. \[ = 3 \ln{\left(x \right)} - \frac{d}{d x} 3 x + 3 \]
   derivative algebra algebraDifferentiate the individual components. Simplify the expression inside the parentheses. Distribute the 3 into the parentheses.✓ Proved
6. \[ = 3 \ln{\left(x \right)} - 3 \frac{d}{d x} x + 3 \]
   constant-multipleFactor out the 3 from the second term.✓ Proved
7. \[ = 3 \ln{\left(x \right)} \]
   derivative algebra simplifyDifferentiate the remaining term. Simplify the expression. Combine the constant terms.✓ Proved