Physicsnut said:
The simplified tags have only been available since December 20.HallsofIvy said:
The derivative of ln(ln x) is 1/(x ln x).
To find the derivative of ln(ln x), you can use the chain rule. First, rewrite ln(ln x) as ln(u), where u = ln x. Then, take the derivative of ln(u), which is 1/u. Finally, multiply by the derivative of u, which is 1/x. This gives us 1/(x ln x) as the derivative of ln(ln x).
Yes, the derivative of ln(ln x) can be simplified to 1/(x ln x), as this is the most simplified form.
The domain of the derivative of ln(ln x) is x > 1, as the natural logarithm function is only defined for positive numbers, and ln x would be undefined for x ≤ 0.
The derivative of ln(ln x) is useful in many real-life applications, such as in economics and finance, where it can be used to calculate marginal revenue and marginal cost. It is also commonly used in physics and engineering to calculate rates of change and growth. Additionally, the derivative of ln(ln x) is an important step in finding the derivatives of other logarithmic functions.