## Introduction to Directional Derivative Calculator

Directional Derivative Calculator with steps is an online tool that can compute the directional derivative of a function at a point in the direction of a vector. In other words, it calculates the rate of change of a function at a point.

Vector derivative calculator is a powerful tool to evaluate the derivative of different kinds of functions. It can also calculate maximal and minimal increase rates.

In mathematics, the directional derivative is difficult to understand because it is used to specify the direction of a given vector. Here we introduce online software that can help the user understand its concept.

## What is a Directional Calculator?

The directional derivative calculator with angle is an online tool which is made to compute the instantaneous rate of change of a function with the vector. It calculates the derivative of a function in the direction of the unit vector.

The term derivative is used for different purposes like the equation of tangent, slope of a line, or linear approximation of a function. The directional derivative is used to find the rate of change of a tangent line in the direction of a vector, which can be confusing while computing manually. The use of the directional derivative calculator with steps makes this concept easier and provides faster results.

## Formula used to Calculate the Directional Derivative

Since directional derivatives are a way to compute slope or rate of change of a tangent line in the direction of a unit vector. To find the directional derivative, you have to find the gradient of the function. Because the gradient of a function gives a surface and unit vector.

Mathematically, directional derivative can be written as,

$$ D_{\hat u} \;f \;=\; {\nabla f} \;. \; {\hat u} $$

Where f is the gradient of the function f and u is the unit vector.

Gradient of a function gives the greatest increase rate of change. To compute gradients, nabla derivatives of the given function must be calculated. In other words you need to compute gradient such as:

$$ {\nabla f}(x,y) \;=\; \frac{df}{dx} {\hat i} \;+ \; \frac{df}{dy} {\hat j} $$

Or in 3 dimensions,

$$ {\nabla f}(x,y) \;=\; \frac{df}{dx} {\hat i} \;+\; \frac{df}{dy} {\hat j} \;+\; \frac{df}{dz} {\hat k} $$

These formulas are used by the vector calculator to evaluate directional derivatives.

## How to Use

There are simple steps of using this tool, these are:

- Enter the function in the “Enter Function” box.
- If you want to compute directional derivative for 2D then choose fx,y and for 3D choose fx,y,z.
- Now write the values for the vector in $$ U_1 \;,\; U_2 $$
- Write x and y coordinates.
- In the last step, click on the calculate button.

As you click on the calculate button, the Directional Derivative Calculator will start processing. It will show the results within a few moments.

## Why to use a Vector Derivative Calculator?

The term directional derivative tells how a function changes with the coordinates. To compute directional derivative, you need to calculate the gradient of the function. If you do it manually, you may get stuck in the middle. But with the use of Directional Derivative Calculator two points, there is no chance to get stuck.

This online calculator helps the students to concentrate on the concept as well as its calculation. So for this purpose, it provides a step-by-step solution. The main reason to use Directional Derivative Calculator with steps is that it is user friendly. It allows you to do practice with different examples.

The impact of technology is increasing in our daily life so you should upgrade your learning resources by using it. You can also consult different tools available on this website.

## Benefits of using the Calculator of Directional Derivative

This free online calculator is a helpful tool in many ways. There are some major advantages of using this tool given bellow:

- It saves your time doing manual calculations.
- An important significance of this tool is that it allows the user to solve more difficult and tricky problems easily.
- Directional Derivative Calculator two points also calculates the gradient of the given function.
- It can handle both 2 & 3 dimension problems efficiently.
- The main idea of directional derivative is based on nabla derivatives. This tool calculates them precisely.
- The Vector Derivative Calculator is a free online tool. You don’t need to subscribe to any package to use it.

**Example:**

Find the directions of maximal and minimal increase using the directional derivative of the given function.

$$ f(x,y) \;=\; sinxcosy \;And\; U\; =\; \frac{\pi}{3} \;,\; \frac{\pi}{3} $$ **Solution:**

In step one, you have to find gradient of fx,y=sinxcosy using nabla derivatives.

$$ \frac{df}{dx} \;=\; cosxcosy $$

And

$$ \frac{df}{dx} \;=\; -sinxsiny $$

Gradient can be written as,

$$ {\nabla f} \;= \; (cosxcosy, \;-sinxsiny) $$

Since the formula for directional derivative is,

$$ D_{\hat u} f \;=\; {\nabla f} \;.\; {\hat u} $$

So, directional derivative in the direction of

$$ U \;=\; \left( \frac{\pi}{3} \;,\; \frac{\pi}{3} \right) $$

is,

$$ D_{\hat u} f \;=\; ( \frac{1}{4} \;,\; \;-\; \frac{3}{4} ) $$

## Other Related Calculators

Calculatores is on a mission to provide best online calculators. There are related calculators on this website which you can use to uplift your learning. These online derivative calculators are:

- Implicit differentiation calculator for solving implicit functions and differentiation.
- Partial derivative calculator with steps for finding partial derivative of a function of several variables.
- Derivative function calculator for calculating derivative of a function.
- Triple derivative calculator to find the third derivative of a function.
- linearization calculator for finding local linear approximation or tangent line approximation.
- Double derivative calculator for calculating the second derivative of a function.
- Chain rule derivative calculator to differentiate composite functions.
- Product rule calculator with steps to differentiate product of two functions.
- Quotient rule calculator to calculate the denominator and the numerator of a derivative function.
- Normal line calculator to calculate perpendicular to the tangent line at the point of tangency.

## FAQ’s

**What is the difference between derivative and directional derivative?**

Derivative is used to calculate the rate of change of a function with respect to an independent variable. Whereas directional derivative is used to calculate instantaneous rate of change in the direction of a vector. It uses a unit vector as a domain.

**What is the use of directional derivatives?**

It is used find the rate of instantaneous change which can be used to define lines and planes that are tangent to a surface at a point.