Derivative of \( \displaystyle e^{\left(2 x + 1\right)^{2}} \)

Problem 2.620 · hard

1. \[ \frac{d}{d x} e^{\left(2 x + 1\right)^{2}} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = e^{\left(2 x + 1\right)^{2}} \frac{d}{d x} \left(2 x + 1\right)^{2} \]
   chainApply the chain rule.✓ Proved
3. \[ = \left(4 x + 2\right) e^{\left(2 x + 1\right)^{2}} \frac{d}{d x} \left(2 x + 1\right) \]
   powerApply the power rule to the exponent.✓ Proved
4. \[ = \left(8 x + 4\right) e^{\left(2 x + 1\right)^{2}} \]
   derivative algebra algebraDifferentiate the inner linear function. Simplify the constants. Rearrange the terms.✓ Proved