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Find the derivative of e^(2x)

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Answer
2e2x\boxed{2e^{2x}}

We can check this result by using the chain rule in reverse to integrate 2e2x2e^{2x}, which brings us back to e2xe^{2x}.

Problem: Find the derivative of e2xe^{2x}, i.e., ddx[e2x]\frac{d}{dx}[e^{2x}].

Steps

  1. Apply the chain rule
    ddx[e2x]=e2x⋅ddx[2x]\frac{d}{dx}[e^{2x}] = e^{2x} \cdot \frac{d}{dx}[2x]
  2. Differentiate the exponent
    e2x⋅2e^{2x} \cdot 2
  3. Rearrange terms
    2e2x2e^{2x}

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