Derivative of \( \displaystyle \left(2 x - 3\right) e^{4 x - 6} \)

Problem 2.480 · medium

1. \[ \frac{d}{d x} \left(2 x - 3\right) e^{4 x - 6} \]
   Start with the derivative of the function.✓ Proved
2. \[ = \left(2 x - 3\right) \frac{d}{d x} e^{4 x - 6} + e^{4 x - 6} \frac{d}{d x} \left(2 x - 3\right) \]
   productApply the product rule.✓ Proved
3. \[ = \left(2 x - 3\right) \frac{d}{d x} e^{4 x - 6} + 2 e^{4 x - 6} \]
   derivativeDifferentiate the first part of the product.✓ Proved
4. \[ = \left(2 x - 3\right) e^{4 x - 6} \frac{d}{d x} \left(4 x - 6\right) + 2 e^{4 x - 6} \]
   chainApply the chain rule to the exponential term.✓ Proved
5. \[ = 4 \left(2 x - 3\right) e^{4 x - 6} + 2 e^{4 x - 6} \]
   derivativeDifferentiate the inner function 4*x - 6.✓ Proved
6. \[ = \left(8 x - 12\right) e^{4 x - 6} + 2 e^{4 x - 6} \]
   algebraDistribute the 4 into the binomial.✓ Proved
7. \[ = \left(8 x - 10\right) e^{4 x - 6} \]
   algebra simplifyFactor out the common exponential term. Simplify the expression inside the parentheses.✓ Proved