Derivative of \( \displaystyle 4 x^{2} \ln{\left(2 x \right)} \)

Problem 2.600 · hard

1. \[ \frac{d}{d x} 4 x^{2} \ln{\left(2 x \right)} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = 4 \frac{d}{d x} x^{2} \ln{\left(2 x \right)} \]
   constant-multiplePull out the constant factor 4.✓ Proved
3. \[ = 4 x^{2} \frac{d}{d x} \ln{\left(2 x \right)} + 4 \ln{\left(2 x \right)} \frac{d}{d x} x^{2} \]
   productApply the product rule.✓ Proved
4. \[ = 4 x^{2} \frac{d}{d x} \ln{\left(2 x \right)} + 8 x \ln{\left(2 x \right)} \]
   powerDifferentiate x**2.✓ Proved
5. \[ = 8 x \ln{\left(2 x \right)} + 2 x \frac{d}{d x} 2 x \]
   chainApply the chain rule to log(2*x).✓ Proved
6. \[ = 8 x \ln{\left(2 x \right)} + 4 x \]
   derivative algebra algebra simplifyDifferentiate 2*x. Simplify the fraction. Simplify x**2/x. Distribute the 4 and simplify.✓ Proved