Derivatives · Exponential & Logarithmic

Derivative of aˣ

\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.

2 worked examples
24 in Derivatives

Worked examples

Find d/dx[2ˣ].

2ˣ · ln 2

Answer: 2ˣ ln 2

1 more worked examplePremium

Find d/dx[10^(2x)].

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Related formulas

Derivative of eˣ

See all 24 Derivatives formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.

Common questions

What is the Derivative of aˣ?

The derivative of a general exponential function aˣ is aˣ times the natural log of the base. It is one of the derivatives formulas in the CalcRef reference.

When does the Derivative of aˣ apply?

The Derivative of aˣ holds under this condition: a > 0 and a ≠ 1.

How do you use the Derivative of aˣ?

Worked example. Find d/dx[2ˣ]. 2ˣ · ln 2. Answer: 2ˣ ln 2.

Practice

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