## Introduction to Chain Rule Calculator:

Chain rule calculator is an online tool that is used to find the differentiation of two or more ** composite functions**. It evaluates the complex function that cannot be solved by other differential methods directly.

Chain rule derivative calculator is a beneficial tool for students, professionals and teachers to get the solution of complex chain rule differential function problems without any error.

## What is Chain Rule?

Chain rule is a process of differentiation, used to solve the **composite function** problems. This method is used when you have a complicated function that cannot be solved with other derivative rule methods (product rule, quotient rule, etc).

Suppose you have a composite function h(x) that can be expressed as h(x) = f(g(x))h(x), where f and g are the functions of x, then the chain rule for derivative function h(x) is.

$$ h’(x) \;=\; f’(g(x)) . g’(x) $$

## How to Calculate Chain Rule?

To **calculate the chain rule**, you need to know the basic method of derivation to identify if the given differential function is a chain rule problem or not. If you don't know about chain rule process then follow the given steps to evaluate chain rule.

**Step 1:**

Identify the chain rule function which should be a composite function.

**Step 2:**

Determine the inner function f(x) and the outer function g(x) for chain rule derivation.

**Step 3:**

Find the derivative of the outer function g`(x), leave the inner function f(x) as constant.

**Step 4:**

Find the derivative of the inner function f`(x) in chain rule differentiation.

**Step 5:**

Then, add the result of derivation of the inner function f`(x) and the outer function g`(x) in the chain rule formula.

$$ h’(x) \;=\; f’(g(x)) . g’(x) $$

**Step 6:**

Simplify the chain rule derivative function after putting the function value in it.

## Solved Example of Chain Rule:

The solved **example** of chain rule problem will help you to understand the method of finding chain rule differential problem.

### Example: find the derivative of the following:

$$ h(x) \;=\; \frac{1}{(3x^2 + 1)^2} $$

**Solution:**

Identify the h(x) and g(x) function.

$$ h(x) \;=\; \frac{1}{(3x^2 + 1)^2} \;=\; (3x^2 + 1)^{-2} $$

$$ g(x) \;=\; 3x^2 + 1 $$

Differentiate the function h(x) and g(x),

$$ h’(x) \;=\; -2(3x^2 + 1)^{-3} $$

$$ g`(x)= 6x $$

Put the h(x) and g(x) in the chain rule formula,

$$ h’(x) \;=\; -2(3x^2 + 1)^{-3} 6x $$

Simplify it,

$$ h’(x) \;=\; \frac{-12x}{(3x^2 + 1)^3} $$

## How to Use Chain Rule Derivative Calculator?

The composite function derivative calculator has a user-friendly interface, you just need to put a differential chain question to get the solution. Follow our guidelines before using it:

**Enter the function**f(x) of chain rule that you want to differentiate in the input box.- Select the variable of differentiation in the input box.
- Check the given derivative value before hitting the calculate button to start the evaluation process.
- The “Calculate” button gives you the solution of your given chain rule differential problem.
- If you want to try our tool for the first time then it is suggested to try the load example to check its working process.
- The “Recalculate” button of derivative of composite function calculator brings back a new page for finding more example solutions of differential problems.

## Output from Chain Rule Solver:

Chain rule calculator with steps gives you the **solution** of chain rule differential question when you give it an input. The results include:

**Result Option**:

When you click on the result option, it gives you the solution of chain rule problem.

**Possible Steps**:

It provides you step by step solution of chain rule differential problem.

## Advantages of Composite Function Derivative Calculator:

This calculator provides you many benefits that you will help to calculate the derivative chain rule problems. These advantages are:

- Chain rule solver is a
**free tool**that enables you to evaluate the chain rule differential problems. - It is a manageable tool that can solve trigonometry, logarithmic, and exponential functions for getting solution of chain rule derivative problem.
- Our chain rule derivative calculator helps you to get a strong hold on chain rule concept by giving you an opportunity to practice complex questions.
- It saves the time that you consume in the calculation of chain rule differential problem.
- Composite derivative calculator provides exact solutions as per your input value and calculate the chain rule differential problems without any error.
- The derivative of composite function calculator is an educational tool that helps you to teach your children, and students in a simple and fun way.