Derivative Calculator

- April 25, 2025
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Calculate the derivative of mathematical functions. This calculator supports common functions including polynomials, trigonometric, logarithmic, and exponential expressions.

Function Input

Evaluation (Optional)

Display Options

About Derivatives

In calculus, the derivative measures how a function changes as its input changes. Specifically, the derivative of a function at a point measures the rate at which the function's output changes per unit change in its input.

Common Differentiation Rules
  • Power Rule: If f(x) = xn, then f'(x) = n·xn-1
  • Sum Rule: If h(x) = f(x) + g(x), then h'(x) = f'(x) + g'(x)
  • Product Rule: If h(x) = f(x)·g(x), then h'(x) = f'(x)·g(x) + f(x)·g'(x)
  • Quotient Rule: If h(x) = f(x)/g(x), then h'(x) = [f'(x)·g(x) - f(x)·g'(x)]/[g(x)]2
  • Chain Rule: If h(x) = f(g(x)), then h'(x) = f'(g(x))·g'(x)
Trigonometric Functions
  • d/dx[sin(x)] = cos(x)
  • d/dx[cos(x)] = -sin(x)
  • d/dx[tan(x)] = sec2(x)
  • d/dx[sec(x)] = sec(x)·tan(x)
  • d/dx[csc(x)] = -csc(x)·cot(x)
  • d/dx[cot(x)] = -csc2(x)
Exponential and Logarithmic Functions
  • d/dx[ex] = ex
  • d/dx[ax] = ax·ln(a)
  • d/dx[ln(x)] = 1/x
  • d/dx[loga(x)] = 1/(x·ln(a))

Understanding the Derivative Calculator

The Derivative Calculator is a handy tool for anyone dealing with functions in Calculus. It allows you to calculate the derivative of various mathematical functions, such as polynomials, trigonometric, logarithmic, and exponential expressions. Whether you’re a student trying to grasp calculus or a professional needing quick calculations, this calculator is designed to help simplify the process.

Inputting Your Function

To get started with the Derivative Calculator, you need to enter your function in the provided input box. You can type expressions like x^2 + sin(x). The calculator supports several types of functions, ensuring you can work with whatever you need. Take your time to enter the function accurately for the best results.

Choosing the Derivative Order

When using the calculator, you can select the order of the derivative you wish to compute. Options range from the first derivative all the way to the fifth derivative. Each choice will provide insights into how the function behaves at different levels of differentiation. This is particularly useful for understanding concepts like concavity and inflection points in calculus.

Evaluating at a Specific Point

If you wish, you can evaluate the derivative at a particular point by checking the evaluation option. This feature allows you to see the exact value of the derivative at a specific x-value, giving you deeper insights into the function's behaviour. You simply need to enter the value of x where you want the evaluation to happen.

Display Options for Your Results

The Derivative Calculator offers various display options to suit your needs. You can choose how you want the output to be presented. Here are some choices you can make:

  • Simplified results
  • Differentiation steps
  • LaTeX format for easy sharing

These options cater to different preferences, whether you want quick outputs or detailed explanations of the calculations.

Graphical Representation of Functions

This calculator does more than just present numeric outputs. It can also generate graphs to visually represent both the original function and its derivative. Seeing these graphs helps in understanding the relationships between the function and its rate of change. You can easily observe how the slope of the tangent line varies at different points along the curve.

Learning About Derivatives

The Derivative Calculator includes a section about derivatives, explaining their significance in calculus. A derivative measures how a function changes as its input changes. This section covers common differentiation rules that can help you understand the underlying principles and apply them in your calculations.

  • Power Rule
  • Sum Rule
  • Product Rule
  • Quotient Rule
  • Chain Rule

These rules are essential tools for anyone looking to master calculus.

Get Started with the Derivative Calculator

Using the Derivative Calculator is simple and intuitive. It’s designed to be user-friendly, making it accessible for beginners while still powerful enough for advanced users. Whether you’re solving calculus problems or just exploring functions, this calculator is a valuable resource. Try it out and see how it can make your calculations smoother!