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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.

  • 2 worked examples
  • 24 in Derivatives

Worked examples

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

Answer: 3e^(3x)

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Find d/dx[x²eˣ].

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Related formulas

Derivative of aˣDerivative of ln(x)

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Common questions

What is the Derivative of eˣ?

The exponential function eˣ is its own derivative -a unique property of the natural exponential. It is one of the derivatives formulas in the CalcRef reference.

How do you use the Derivative of eˣ?

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

Practice

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