## Introduction to Logarithmic Differentiation Calculator:

Logarithmic differentiation calculator is the best source for finding the differentiation of a function using the **logarithmic rules**. It is used for log properties function so it cannot be solved with derivative rules directly.

If you want to solve the logarithmic differentiation problem easily, then this tool is made for you as it provides you a complete solution for your given function without any error.

## What is Logarithmic Differentiation?

Logarithmic differentiation is a method that is used in calculus to **differentiate functions** that are not solved by using standard differentiation rules, like product rule, quotient rule, or chain rule.

This type of function follows logarithmic rules so it uses the natural log to simplify the given function. You can easily solve it with usual differential rules. By using this method you can handle different types of complicated derivative questions without any difficulty.

## How to Do Logarithmic Differentiation?

Logarithmic differentiation method can **simplify the differentiation** process and give you the solution of given functions. Here is a step-by-step explanation of how to calculate the logarithmic differentiation function.

**Step 1**: Suppose you have a function y that depends on x, which is given as y = f(x).

**Step 2**: Implement the logarithm on both sides of the given function such as:

$$ ln\; y \;=\; ln\; (f(x)) $$

**Step 3**: Now, differentiation the equation with respect to x. You can apply any differential rule as per the types of function.

**Step 4**: Solve the given function after applying the derivation rule and you get the solution of logarithmic problem easily.

If you want to solve logarithmic differentiation problems without doing any calculations, try our derivative of log calculator. It's easy to use and provides accurate solutions in seconds!

## Solved Example of Logarithmic Differentiation Function:

The given solved **example** will give you conceptual clarity about the logarithmic differential function concept.

### Example: Determine the derivative of:

$$ y \;=\; (2x^4 + 1)^{tan\; x} $$

**Solution**:

Take the log on both sides,

$$ ln\; (y) \;=\; ln\; (2x^4 + 1)^{tan\; (x)} $$

$$ ln\; (y) \;=\; tan\; (x) ln\; (2x^4 + 1) $$

Different the log function with respect to x,

$$ \frac{1}{y} \frac{dy}{dx} \;=\; sec^2 (x) ln\; (2x^4 + 1) + \frac{8x^3}{2x^4 + 1} . tan (x) $$

Simplify it to get solution of given function,

$$ \frac{dy}{dx} \;=\; y . \left(sec^2 (x) ln (2x^4 + 1) + \frac{8x^3}{2x^4 + 1} . tan (x) \right) $$

Replace y with original value in solution,

$$ \frac{dy}{dx} \;=\; (2x^4 + 1)^{tan (x)} \left(sec^2 (x)\; ln (2x^4 + 1) + \frac{8x^3}{2x^4 + 1} . tan (x) \right) $$

## How to Use the Log Differentiation Calculator?

Log derivative calculator has a simple design that is used for calculating the complex logarithm function derivation. Before using this tool, follow the given steps that helps in finding the solution of logarithmic derivation. These steps are:

- Enter the logarithmic function for differentiation in the input field.
- Add the logarithmic function differential variable in its input field.
- Review your function before clicking on the calculate button to avoid errors.
- Click on the ‘
**Calculate**’ button to get the solution of logarithmic function. - Recalculate button of logarithmic derivative calculator will bring you back to home page for doing more calculations of the logarithmic function.

## Output From Logarithmic Differentiation Calculator With Steps:

Derivative of log calculator gives the **result** of logarithmic function which includes as:

**Solution Option:**

It gives you a solution of given log function differentiation.

**Possible Step Option:**

It provides you step by step solution of logarithmic function.

**Plot Section:**

It shows a graph as per your logarithmic differential result which helps in better understanding.

## Why Choose our Logarithmic Differentiation Calculator:

The log differentiation calculator gives many advantages when you use it to solve the different types of functions, especially the complex logarithmic differentiation functions. The benefits are:

- It is a reliable tool that provides you
**accurate solutions**whenever you use it. - Log derivative calculator is an adaptable tool for everyone because you can use it through electronic devices like laptops, computers tablets, etc.
- It is a learning tool that helps students to learn the concept of logarithmic differentiation function easily.
- Logarithmic derivative calculator saves time and effort that you put in solving lengthy calculations as it gives you results quickly.
- Our tool is free of cost so you do not need to pay anything for the calculation.
- Logarithmic differentiation calculator with steps takes you away from any trouble which you encounter in solving logarithmic derivation function manually.