Derivative of \( \displaystyle \frac{3 x^{2} \left(2 \ln{\left(x \right)} - 1\right)}{4} \)

Problem 2.663 · hard Beautiful

1. \[ \frac{d}{d x} \frac{3 x^{2} \left(2 \ln{\left(x \right)} - 1\right)}{4} \]
   Start with the derivative of the function.✓ Proved
2. \[ = \frac{3 \frac{d}{d x} x^{2} \left(2 \ln{\left(x \right)} - 1\right)}{4} \]
   constant-multiplePull out the constant factor 3/4.✓ Proved
3. \[ = \frac{3 x^{2} \frac{d}{d x} \left(2 \ln{\left(x \right)} - 1\right)}{4} + \frac{3 \left(2 \ln{\left(x \right)} - 1\right) \frac{d}{d x} x^{2}}{4} \]
   productApply the product rule.✓ Proved
4. \[ = \frac{3 x^{2} \frac{d}{d x} \left(2 \ln{\left(x \right)} - 1\right)}{4} + \frac{3 x \left(2 \ln{\left(x \right)} - 1\right)}{2} \]
   derivativeDifferentiate x**2.✓ Proved
5. \[ = \frac{3 x^{2} \frac{d}{d x} \ln{\left(x \right)}}{2} + \frac{3 x \left(2 \ln{\left(x \right)} - 1\right)}{2} \]
   derivativeDifferentiate the terms inside the parentheses.✓ Proved
6. \[ = \frac{3 x \left(2 \ln{\left(x \right)} - 1\right)}{2} + \frac{3 x}{2} \]
   derivative algebraDifferentiate log(x). Simplify the term x**2 * (2/x).✓ Proved
7. \[ = 3 x \ln{\left(x \right)} \]
   algebra simplify simplifyDistribute 2*x into the parentheses. Combine like terms. Final simplification.✓ Proved