Derivative of ln x
Derivative of the natural log.
Key idea
Derivative of the natural log.
In depth
d/dx ln x = 1/x for x > 0. It follows from the inverse function relationship with eˣ. More generally d/dx ln(g(x)) = g′(x)/g(x).
Worked example
d/dx ln(x²+1) = 2x/(x²+1).
Formula
Real-world uses
- Calculating the rate of change of log-based measures such as information and sound levels
Common mistake
Forgetting the domain x > 0 or the inner derivative.
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 Derivative of ln x?
Derivative of the natural log. It is a topic at the advanced level in Calculus.
What is the formula for Derivative of ln x?
The key formula is (ln x)′ = 1/x.
Where is Derivative of ln x used in real life?
Real-world examples: Calculating the rate of change of log-based measures such as information and sound levels.
What should I learn before Derivative of ln x?
Make sure you are comfortable with Derivative of eˣ, the previous topic in Calculus.
What is a common mistake with Derivative of ln x?
Forgetting the domain x > 0 or the inner derivative.
How can I practise Derivative of ln x?
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 Derivative of ln x?
Move on to Derivatives of Inverse Trig next.
Related advanced topics in Calculus
- Idea of a Limit – The value a function approaches as the input approaches a point.
- One-Sided Limits – Left and right limits must agree for the limit to exist.
- Limit Laws – Limits of sums, products and quotients are computed from the parts.
- Factoring and Rationalizing Limits – Remove 0/0 indeterminacy with algebra.
- Limits at Infinity – End behaviour of functions.
- Infinite Limits and Asymptotes – Function values grow without bound near a vertical asymptote.