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Derivative of Logarithmic Functions
Learn the rules for differentiating ln x and log base a functions, including the chain rule and logarithmic differentiation, with clear worked examples.
What You'll Learn
The derivative of ln x is 1 over x, and this idea extends to any log base through a change-of-base style formula
For a logarithm of a function u of x, the chain rule gives the derivative of ln u as u prime over u
Logarithmic differentiation turns products, quotients, and variable exponents into sums before you differentiate
Common practice problems ask for the derivatives of x times ln x, ln of 2x, and ln of 1 over x
Log properties like ln of a over b equals ln a minus ln b make a derivative much easier to find before applying any rule
What You'll Practice
1
Finding derivatives of log functions with various bases like log(x)
2
Differentiating common logs and natural logs of trigonometric functions
3
Applying chain rule to natural log of polynomials and composite expressions
4
Simplifying complex derivatives involving radicals and natural logarithms
Why This Matters
Mastering derivatives of logarithmic functions is essential for calculus success. You'll use these techniques throughout differential calculus, optimization problems, and growth/decay models in science and economics. Natural log derivatives are particularly powerful for simplifying complex differentiation problems.
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Logarithmic Differentiation
Natural Logarithm
Chain Rule
Power Rule
Trigonometric Derivatives
Calculus
Derivatives
IL Curriculum Aligned