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

Problem 2.174 · medium

1. \[ \frac{d}{d x} e^{2 x - 3} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = e^{2 x - 3} \frac{d}{d x} \left(2 x - 3\right) \]
   chainApply the chain rule.✓ Proved
3. \[ = \left(- \frac{d}{d x} 3 + \frac{d}{d x} 2 x\right) e^{2 x - 3} \]
   sumApply the difference rule for derivatives.✓ Proved
4. \[ = 2 e^{2 x - 3} \]
   derivative simplifyEvaluate the derivatives of the individual terms. Simplify the final expression.✓ Proved