This tool helps you calculate the derivative of multivariable functions using the chain rule.

## How to Use the Multivariable Chain Rule Calculator

This calculator helps compute the derivative of a composition of functions using the chain rule for multivariable functions.

### Steps

- Enter the outer function f(u) in the given field. Use ‘^’ for powers. For example, enter ‘u^3 + 2u’ for the function f(u) = u^3 + 2u.
- Enter the inner function u(x, y) in the given field. For example, enter ‘x^2 + y’ for the function u(x, y) = x^2 + y.
- Enter the function x(t). For example, enter ‘t^2’ for x(t) = t^2.
- Enter the function y(t). For example, enter ‘3t’ for y(t) = 3t.
- Enter the point ‘t’ at which you want to evaluate the derivative.
- Click the ‘Calculate’ button to compute the derivative.

The result will be displayed in the ‘Result’ field.

### Limitations

Currently, this calculator can handle polynomial and basic trigonometric functions. It does not support implicit differentiation or parametric equations involving more complex functions such as logarithmic, exponential, or advanced trigonometric functions.

## Use Cases for This Calculator

### Calculating multivariable chain rule for a simple function

Use this calculator to find the multivariable chain rule for functions that involve multiple variables. Enter the function and respective variables to easily determine the derivative.

### Applying multivariable chain rule with nested functions

When dealing with nested functions, simply input the functions within each other and include the appropriate variables. This calculator will help you navigate through complex nested functions effortlessly.

### Finding multivariable chain rule with trigonometric functions

If your function involves trigonometric functions, enter the trigonometric expression along with the variables to calculate the multivariable chain rule accurately. This tool streamlines the process for you.

### Considering multiple variables in the chain rule

For functions with more than one variable, this calculator enables you to account for all variables in the multivariable chain rule. Enter the function and associated variables to get the derivative with respect to each variable.

### Determining the multivariable chain rule with exponential functions

Whether your function contains exponential functions, this calculator handles them efficiently. Input the exponential expression and the variables to obtain the derivative using the multivariable chain rule.

### Verifying multivariable chain rule calculations

After performing manual calculations for the multivariable chain rule, use this calculator to double-check your work. Input the function and variables to confirm your derivative calculations.

### Simplifying multivariable chain rule calculations

This calculator simplifies the computation process for multivariable chain rule problems. Input the function and corresponding variables to quickly arrive at the derivative values.

### Exploring multivariable chain rule with composite functions

If your function consists of composite functions, this calculator is your go-to tool. Input the composite function components and variables to effortlessly compute the multivariable chain rule.

### Handling multivariable chain rule for polynomial functions

For polynomial functions involving multiple variables, use this calculator to seamlessly determine the multivariable chain rule. Enter the polynomial function along with the variables for accurate derivative calculations.

### Mastering multivariable chain rule for real-world applications

Apply the multivariable chain rule to real-world scenarios with ease using this calculator. Input the function representing the problem and relevant variables to obtain the derivative for practical applications.