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

Problem 2.470 · hard

1. \[ \frac{d}{d x} e^{\left(x - 3\right)^{2}} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = e^{\left(x - 3\right)^{2}} \frac{d}{d x} \left(x - 3\right)^{2} \]
   chainApply the chain rule.✓ Proved
3. \[ = \left(2 x - 6\right) e^{\left(x - 3\right)^{2}} \frac{d}{d x} \left(x - 3\right) \]
   powerApply the power rule to the inner function.✓ Proved
4. \[ = \left(2 x - 6\right) e^{\left(x - 3\right)^{2}} \]
   derivative algebra algebraDifferentiate the inner linear term. Distribute the 2. Rearrange the terms.✓ Proved