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Derivative calculator

Find the theoretical value of a European call or put option from the stock price, strike, volatility and time to expiry using the Black-Scholes model.

How it works Report a problem

Options Intelligence Pro

Black-Scholes quantitative modeling and Greek sensitivity

Underlying & Strike
$
$
Market Dynamics
Theoretical Price
$0.00
Delta
0.00
Gamma
0.00
Theta
0.00
Vega
0.00

A derivative measures how fast something changes: the slope of a function at a point. In finance it appears as marginal cost, marginal revenue and sensitivity to price or rate changes. This calculator differentiates the function you enter and shows the resulting expression.

How to use this calculator

  • Enter the function in terms of x, such as x^3 + 2x.
  • Press calculate to see the derivative.
  • Use the result to find the rate of change at a specific value of x.

The rules doing the work

The power rule turns x^n into n·x^(n−1). Sums differentiate term by term, constants vanish, and products and quotients use their own rules when functions multiply or divide. The chain rule handles nested functions, such as the square of an expression. Knowing which rule fired makes the result easier to trust and to reuse.

Frequently asked questions

What does a derivative of zero mean?
At that point the function is momentarily flat — often a maximum, a minimum, or a turning point worth investigating.
What is the difference between a derivative and a differential?
The derivative is a function giving the rate of change; a differential is the small change estimated from it (dy ≈ f'(x)·dx) for a small step in x.
Where is this used in finance?
Marginal analysis (cost and revenue of one more unit), option Greeks such as delta, and duration, which measures how a bond's price responds to rate changes.