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Derivatives · Exponential & Logarithmic

Derivative of aˣ

ddx[ax]=axln⁡a\frac{d}{dx}[a^x] = a^x \ln a

The derivative of a general exponential function aˣ is aˣ times the natural log of the base.

Conditions. a > 0 and a ≠ 1.

Worked examples

Find d/dx[2ˣ].
  1. 2ˣ · ln 2

Answer: 2ˣ ln 2

Find d/dx[10^(2x)].
  1. Chain rule: 10^(2x) · ln 10 · 2 = 2 · 10^(2x) · ln 10

Answer: 2 · 10^(2x) ln 10

Related formulas

Derivative of eˣ

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