Logarithmic Differentiation Calculator

Work out logarithmic differentiation instantly with clear inputs, formula shown and shareable results.

About Logarithmic Differentiation Calculator

Taking logarithms turns a variable power into a product: ln y = g·ln f. Differentiating gives y'/y = g'·ln f + g·f'/f, so y' = y(g'·ln f + g·f'/f).

Formula

Logarithmic differentiation

y = f^g ⇒ y' = f^g · (g'·ln f + g·f'/f)

Worked example

With the default values below, Logarithmic Differentiation Calculator returns dy/dx of 184.72283911. Change any input above and every figure here is recalculated in your browser.

Inputs used

Base function value f(x)minimum 0: 4
f'(x): 2
Exponent g(x): 3
g'(x): 1

Results

dy/dx: 184.72283911
y = f(x)^g(x): 64.00000000
y'/y: 2.88629436
Contribution from the exponent changing: 88.72283911

Step by step

1Values used
2Logarithmic differentiation
3dy/dx= 184.72283911
4y = f(x)^g(x)= 64.00000000
5y'/y= 2.88629436
6Contribution from the exponent changing= 88.72283911

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

With f = 4, f' = 2, g = 3, g' = 1?

y = 64 and y'/y = ln 4 + 3 × 0.5 = 2.8862944, so y' ≈ 184.7228.

Why not just use the power rule?

The power rule assumes a constant exponent. When the exponent varies, both the base and the exponent contribute.