Logarithmic Differentiation
Take logs before differentiating products and powers.
Key idea
Take logs before differentiating products and powers.
In depth
For products, quotients, or functions like xˣ, take ln of both sides first. Logs turn products into sums and powers into multipliers, then differentiate implicitly.
Worked example
y = xˣ: ln y = x ln x; y′/y = ln x + 1; y′ = xˣ(ln x + 1).
Real-world uses
- Differentiating complicated power formulas in economics and science models
Common mistake
Forgetting to multiply by y at the end.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Logarithmic Differentiation?
Take logs before differentiating products and powers. It is a topic at the expert level in Calculus.
Where is Logarithmic Differentiation used in real life?
Real-world examples: Differentiating complicated power formulas in economics and science models.
What should I learn before Logarithmic Differentiation?
Make sure you are comfortable with Implicit Differentiation, the previous topic in Calculus.
What is a common mistake with Logarithmic Differentiation?
Forgetting to multiply by y at the end.
How can I practise Logarithmic Differentiation?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Logarithmic Differentiation?
Move on to Higher-Order Derivatives next.
Related expert topics in Calculus
- Derivatives of Inverse Trig – Derivatives of arcsin, arccos, arctan.
- Implicit Differentiation – Differentiate both sides of F(x,y)=0 treating y as a function of x.
- Related Rates – Link rates of change of connected quantities.
- Linear Approximation – Approximate f near a using its tangent line.
- Differentials – Use dy = f′(x)dx for small changes.
- Second Derivative Test – f″ > 0 means concave up; f″ < 0 concave down.