Derivative Calculator

Find the derivative of any function with step-by-step explanations and interactive graphs.

Instant derivatives with **steps** and **interactive graphs**. Enter any function to see how its rate of change behaves.

✓ Step-by-Step✓ Interactive Graph✓ Trig & Exponents✓ Power, Product, Chain Rules

Enter Function f(x)

Function

f(x) =

Graph Range (±5)

Examples:

Graph Evaluation

Computed Derivative

\frac{d}{dx}(x^2) = 2x

What is Derivative Calculator?

What is a Derivative?

In calculus, the **derivative** measures how a function changes as its input changes. Geometrically, it represents the **slope of the tangent line** to the graph of the function at any point.

f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

Formula & Calculation

Common Differentiation Rules

Power Rule $\frac{d}{dx}(x^n) = nx^{n-1}$
Sum Rule $(f + g)' = f' + g'$
Product Rule $(fg)' = f'g + fg'$
Chain Rule $\frac{d}{dx}f(g(x)) = f'(g(x))g'(x)$

Example Calculation

Velocity Example

If position is given by $s(t) = t^2$ , then velocity is the derivative:

v(t) = s'(t) = 2t

Related Tools

Frequently Asked Questions

Why calculate derivatives?

Derivatives are essential in physics (velocity, acceleration), economics (marginal cost), and optimization (finding maximum efficiency).