find the derivative calculator

What this derivative calculator does

This tool helps you quickly find the derivative of a mathematical function. If you are studying calculus, checking homework, preparing for an exam, or validating symbolic math in engineering and economics work, this calculator gives you a fast result with clean notation.

You can enter expressions such as x^2, sin(x), log(x), or combinations like x^3 + 2*x - cos(x). The calculator computes f′(x), and if you provide a numeric point, it also evaluates the derivative at that value.

How to use it

1) Enter a function

Type your function into the input box using standard calculator syntax. Multiplication should be explicit when helpful (for example, use 2*x), and powers are entered with the caret symbol ^.

2) Choose the variable

By default, the derivative is taken with respect to x. You can change this to another variable like t or y if your expression uses it.

3) Optional: evaluate at a point

If you want a slope value at a specific input, provide a number in the point field. Example: if your function is x^2 and the point is 3, the derivative value is 6.

Supported expression examples

• Polynomials: x^4 - 3*x + 7
• Trigonometric: sin(x), cos(x), tan(x)
• Exponential and logarithmic: exp(x), log(x)
• Radicals: sqrt(x)
• Combinations with chain rule: sin(x^2), exp(3*x + 1)

Quick calculus refresher

Power rule

If f(x) = xⁿ, then f′(x) = n*x^n-1. Example: derivative of x^5 is 5*x^4.

Product rule

For f(x) = u(x)v(x), derivative is u′(x)v(x) + u(x)v′(x). This matters when you multiply two variable expressions, like x^2*sin(x).

Chain rule

For a composite function f(g(x)), derivative is f′(g(x))*g′(x). Example: derivative of sin(x^2) is cos(x^2)*2*x.

Common input mistakes and fixes

• Missing parentheses: write sin(x), not sin x.
• Wrong logarithm name: use log(x) for natural logarithm.
• Invalid point: point must be numeric if provided.
• Empty expression: enter a valid function before calculating.

Why this is useful

Derivatives represent rates of change. In physics, they model velocity and acceleration. In economics, they capture marginal cost and marginal revenue. In machine learning and optimization, derivatives guide gradient-based methods. A reliable derivative calculator helps you move faster and reduces algebra mistakes.

Final notes

This calculator is excellent for symbolic differentiation practice and quick verification. For best results, enter expressions with clear syntax and test a few known examples first. If you are learning calculus, try predicting the derivative manually, then compare with the tool to build confidence.