Tangent Line Calculator

About the Tangent Line Calculator

The Tangent Line Calculator computes the equation of the tangent line to a function f(x) at a point x = a. It supports simple functions like x^2, sin(x), cos(x), e^x, and ln(x). This tool is ideal for calculus students, teachers, and professionals.

• Features:
  • Computes the tangent line y = mx + b at a point x = a.
  • Supports polynomials (e.g., x^2), trigonometric functions (sin, cos), exponentials (e^x), and logarithms (ln).
  • 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 for understanding slopes, linear approximations, and function behavior.
• How to Use
  • Enter a function and point (e.g., x^2; 2).
  • Use the keypad to insert digits, variable (x), operators, and functions (sin, cos, ln, e^).
  • Click "Calc" to compute the tangent line 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 defined and differentiable at the point (e.g., avoid discontinuities like 1/x at x = 0).
  • Use * for multiplication and / for division in complex expressions (e.g., sin(x)/x).
  • Point format: Enter a number after a semicolon (e.g., x^2; 2).
  • The calculator may not handle complex functions or undefined derivatives accurately.
• Examples
  • Example 1: Polynomial: Tangent to f(x) = x^2 at x = 2
    • Input: x^2; 2
    • Steps: Evaluate f(2) = 4, compute f'(2) = 4, find y = 4x - 4.
    • Result: Tangent line: y = 4x - 4
  • Example 2: Trigonometric: Tangent to f(x) = sin(x) at x = 0
    • Input: sin(x); 0
    • Steps: Evaluate f(0) = 0, compute f'(0) = 1, find y = x.
    • Result: Tangent line: y = x
  • Example 3: Exponential: Tangent to f(x) = e^x at x = 0
    • Input: e^x; 0
    • Steps: Evaluate f(0) = 1, compute f'(0) = 1, find y = x + 1.
    • Result: Tangent line: y = x + 1

Calculate tangent lines with ease using this Tangent Line Calculator. Share or embed it on your site!