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Derivatives · Exponential & Logarithmic

Derivative of eˣ

ddx[ex]=ex\frac{d}{dx}[e^x] = e^x

The exponential function eˣ is its own derivative -a unique property of the natural exponential.

Worked examples

Find d/dx[e^(3x)].
  1. By chain rule: e^(3x) · 3 = 3e^(3x)

Answer: 3e^(3x)

Find d/dx[x²eˣ].
  1. Product rule: 2x · eˣ + x² · eˣ = eˣ(2x + x²) = xeˣ(2 + x)

Answer: xeˣ(x + 2)

Related formulas

Derivative of aˣDerivative of ln(x)

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