Mathematical formulas

Differential Calculus

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1Notation, functions and domains
2Limits
3Continuity
4Derivative and geometric interpretation
5Differentiation rules
6Higher-order derivatives
7Mean value theorem
8Function analysis
9Optimization
10Linear approximations and differentials
11Taylor series (introduction)
12L'Hôpital and indeterminate limits
13Implicit and related functions
14Related rates
15Graphs and asymptotic behavior
16Guide to differentiate and analyze
AAppendix A: extended derivative table

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Differential Calculus
Logarithmic differentiation
Formula

5.8. Logarithmic differentiation

Formula

In 5.8. Logarithmic differentiation

Formula

y=f(x)^{g(x)} \Rightarrow \ln y=g(x)\ln f(x),\qquad f(x)>0

Tags

Differential calculus
Derivative
Derivative formula
Rule
Logarithmic differentiation

Detail

First step to differentiate

f^g

with variable exponent (requires

f(x)>0

where

\ln

is applied).

Explore the idea

Explore the idea

Variables

$x$ Independent variable
$f$ Function
$g$ Second function or inner composition
$y$ Dependent variable
$\ln$ Natural logarithm

Conditions

$f(x)>0$

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Related formulas

Related
Formula
$\frac{d}{dx}[\ln|f(x)|]=\frac{f'(x)}{f(x)},\qquad f(x)\neq0$
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