Differentiate $e^{3x}$.

How we read your problem

Find the derivative of e^(3x) with respect to x.

Step-by-step solution

1. 1

   Exponential rule: d/dx[eᵘ] = eᵘ·u′

   $$\frac{d}{dx}\left[{e}^{3x}\right] = 3{e}^{3x}$$
2. 2

   Constant multiple rule

   $$\frac{d}{dx}\left[3x\right] = 3$$
3. 3

   Combine and simplify

   $$f'(x) = 3{e}^{3x}$$

The derivative is built from the outside in: sums split into terms, constants factor out, products and quotients use their rules, and every composite function multiplies by the derivative of its inside (chain rule).

Verification

• Cross-checked numerically against an independent symbolic differentiator at 8 sample points ✓