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📈 Derivative Calculator

Calculate derivatives of functions with step-by-step solutions using common differentiation rules

Limited Function Support

This calculator currently supports ONLY these function types:

  • Polynomials: x², 3x³, 2x⁴ + 5x² - 3
  • Basic trig: sin(x), cos(x), tan(x)
  • Exponential: eˣ
  • Logarithm: ln(x)
  • Simple products: x·sin(x), 2x·cos(x)

NOT supported: Composite functions like sin(2x), nested functions like ln(x²), complex chain rule, or advanced quotient rule.

Enter Function

Supported: x^n, sin(x), cos(x), tan(x), e^x, ln(x), sqrt(x). Use * for multiplication (e.g., 2*x not 2x).

Common Derivatives Reference

d/dx(xⁿ) = n·xⁿ⁻¹
Power Rule
d/dx(sin(x)) = cos(x)
Sine
d/dx(cos(x)) = -sin(x)
Cosine
d/dx(tan(x)) = sec²(x)
Tangent
d/dx(eˣ) = eˣ
Natural Exponential
d/dx(ln(x)) = 1/x
Natural Logarithm
d/dx(√x) = 1/(2√x)
Square Root
d/dx(c) = 0
Constant

How to Use This Calculator

  1. Enter your function using standard notation (e.g., x^2, sin(x), e^x)
  2. Use * for multiplication (e.g., 2*x instead of 2x)
  3. Select the derivative order (first, second, or third derivative)
  4. Click "Calculate Derivative" to see the result
  5. Review the derivative and any step-by-step explanations provided

Understanding Derivatives

What is a Derivative?

The derivative represents the rate of change of a function. Geometrically, it's the slope of the tangent line to the function at any point.

Power Rule

For any power of x, bring down the exponent and subtract one from the exponent: d/dx(xⁿ) = n·xⁿ⁻¹

Product Rule

When differentiating a product of two functions: d/dx(f·g) = f'·g + f·g'

Chain Rule

For composite functions: d/dx(f(g(x))) = f'(g(x))·g'(x)

Quotient Rule

When differentiating a quotient: d/dx(f/g) = (f'·g - f·g')/g²

Frequently Asked Questions

What functions can this calculator differentiate?

This calculator supports polynomials, trigonometric functions (sin, cos, tan), exponential functions (eˣ), natural logarithm (ln), and basic combinations using addition, subtraction, multiplication, and division.

How do I enter multiplication?

Always use the asterisk (*) symbol for multiplication. For example, write "2*x" instead of "2x", and "x*sin(x)" instead of "x sin(x)".

Can I calculate higher-order derivatives?

Yes! You can calculate up to the third derivative (f'''(x)). Simply select the desired derivative order before calculating.

Is this tool free to use?

Yes! This tool is completely free with no hidden costs, subscriptions, or limitations. Use it as often as you need.

Is my data private?

Absolutely. All processing happens locally in your browser. Your data never leaves your device and is not stored on any server.