Derivative Calculator

About the Derivative Calculator

The Derivative Calculator computes the derivative \( f'(x) \) of a function \( f(x) \) using symbolic differentiation. It supports functions like \( x^2 \), \( \sin(x) \), or \( e^x \). This tool is ideal for calculus students, teachers, and professionals.

• Features:
  • Computes the derivative \( f'(x) \) of the input function (e.g., \( f(x) = x^2 \rightarrow f'(x) = 2x \)).
  • Supports polynomials, trigonometric functions (sin, cos), exponentials (e^x), and logarithms (ln).
  • Displays results in LaTeX format for clarity.
  • Keypad for easy input with digits, variable (\( x \)), operators (+, -, *, /, ^), and functions (sin, cos, ln, e^).
  • Clear and backspace functionality, with a "Copy" button for results.
• Practical Applications: Useful in calculus, physics, and engineering for finding rates of change, slopes, and optimization.
• How to Use
  • Enter a function (e.g., \( x^2 \), \( \sin(x) \), \( e^x \)).
  • Use the keypad to insert digits, variable (\( x \)), operators, and functions (sin, cos, ln, e^).
  • Click "Calc" to compute the derivative and view the result, then use "Copy" to copy the result.
  • Use "Clear" to reset, or "⌫" to delete the last character.
  • Share or embed the calculator using the action buttons.
• Helpful Tips
  • Ensure the function is differentiable (e.g., avoid undefined operations like division by zero).
  • Use * for multiplication and / for division in complex expressions (e.g., \( 2*x \), not \( 2x \)).
  • Use parentheses for function arguments (e.g., \( \sin(x) \), not \( \sin x \)).
• Examples
  • Example 1: Polynomial: \( x^2 \)
    • Input: \( x^2 \)
    • Result: Derivative \( f'(x) = 2x \).
  • Example 2: Trigonometric: \( \sin(x) \)
    • Input: \( \sin(x) \)
    • Result: Derivative \( f'(x) = \cos(x) \).
  • Example 3: Exponential: \( e^x \)
    • Input: \( e^x \)
    • Result: Derivative \( f'(x) = e^x \).
  • Example 4: Logarithmic: \( \ln(x) \)
    • Input: \( \ln(x) \)
    • Result: Derivative \( f'(x) = \frac{1}{x} \).

Compute derivatives with ease using this Derivative Calculator. Share or embed it on your site!