How Do You Derive f(x) = 1/(ln(x)^2)?

Thread starter christinee112
Start date Apr 28, 2012
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Confused Derivatives

In summary, a derivative is defined as the instantaneous rate of change of a function at a specific point, and can be found using various rules such as the power rule, product rule, quotient rule, or chain rule. A derivative function is a function that describes the derivative of the original function at every point. Common mistakes when finding derivatives include forgetting to apply the chain rule, neglecting to use the product or quotient rule when necessary, and making arithmetic errors. Finding derivatives is important because it allows us to understand the behavior of a function and is essential in many areas of mathematics and science. It is also used to solve optimization problems and model real-world phenomena.

Apr 28, 2012

christinee112

Homework Statement

Find the derivative of f(x):
f(x)= 1/ ((ln(x)^2))

Homework Equations

f(x)= ln(x)
f'(x)= 1/((ln(x))

The Attempt at a Solution

Dx(1/ln(x)^2) =
Dx((ln(x))^-2)=
-2*(ln(x)^-3) * Dx(ln(x)) =
-2*(ln(x)^-3) * 1/x =
-2/(x*ln(x)^3)

Are these the correct steps? I'm getting myself confused

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Apr 28, 2012

BrownianMan

This is correct.

Related to How Do You Derive f(x) = 1/(ln(x)^2)?

1. What is the definition of a derivative?

The derivative of a function f(x) at a point x is defined as the instantaneous rate of change of f(x) at x, or the slope of the tangent line to the graph of f(x) at x.

2. How do I find the derivative of a function?

To find the derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule. These rules allow you to find the derivative of a function by manipulating the function and its variables.

3. What is the difference between a derivative and a derivative function?

A derivative is the instantaneous rate of change of a function at a specific point, while a derivative function is a function that describes the derivative of the original function at every point. In other words, a derivative function is the collection of all the derivatives of a function at every point.

4. What are some common mistakes when finding derivatives?

Some common mistakes when finding derivatives include forgetting to apply the chain rule, neglecting to use the product or quotient rule when necessary, and making arithmetic errors. It is also important to pay attention to domain restrictions and make sure to apply rules correctly for different types of functions (e.g. polynomial, trigonometric, exponential, etc.).

5. Why is finding derivatives important?

Finding derivatives is important because it allows us to understand the behavior of a function, such as its rate of change, concavity, and extremum points. Derivatives are also essential in many areas of mathematics and science, including physics, engineering, economics, and more. Additionally, derivatives are used to solve optimization problems and model real-world phenomena.