Derivative of \( \displaystyle e^{9 x^{2} + 1} \)

Problem 2.492 · hard

1. \[ \frac{d}{d x} e^{9 x^{2} + 1} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = e^{9 x^{2} + 1} \frac{d}{d x} \left(9 x^{2} + 1\right) \]
   chainApply the chain rule.✓ Proved
3. \[ = \left(\frac{d}{d x} 1 + \frac{d}{d x} 9 x^{2}\right) e^{9 x^{2} + 1} \]
   sumDifferentiate the sum inside the parentheses.✓ Proved
4. \[ = 9 e^{9 x^{2} + 1} \frac{d}{d x} x^{2} \]
   derivativeDifferentiate each term separately.✓ Proved
5. \[ = 18 x e^{9 x^{2} + 1} \]
   power simplifyApply the power rule to x**2. Simplify the final expression.✓ Proved