Derivative Calculator

Differentiate a function, identify each rule, and simplify the result one step at a time.

Drag & drop or upload an image or PDF

Enter a derivative, such as d/dx [x^2 e^x]

Try an example

Read the structure before differentiating

A derivative measures instantaneous change. For a smooth graph, it is the slope of the tangent line. The calculation depends on how the function is built, so a product, quotient, or composition needs more than the power rule.

Enter the function and say which variable to use. You can also request a second or higher derivative, or ask for the derivative at a particular point. The result keeps the rule names beside the algebra so you can see why each term appears.

How to use the derivative calculator

Enter the problem as written

Type or paste the full expression. You can also upload a clear photo or PDF and check the extracted text before solving.

Read the working, not only the answer

Each transformation is separated and explained so you can compare it with your own method.

Ask about any step

Continue in the same solution to request another method, check a restriction, or ask why a rule applies.

The chain rule

Differentiate the outside function, keep the inside expression in place, then multiply by the derivative of the inside.

\frac{d}{d x} f (g (x)) = f^{'} (g (x)) g^{'} (x)

A reliable way to work through it

Identify the outer operation

Decide whether the function is a sum, product, quotient, or composition before applying a rule.

Differentiate each layer

Use the power, product, quotient, and chain rules in the order set by the function's structure.

Simplify and check the domain

Factor or combine terms when helpful, but keep restrictions from roots, logarithms, and denominators.

Worked example

Find the derivative of x²eˣ

u = x^{2}, v = e^{x}

Treat the expression as a product of two functions.

u^{'} = 2 x, v^{'} = e^{x}

Differentiate each factor.

(uv)^{'} = u^{'} v + u v^{'}

Apply the product rule.

\frac{d}{d x} (x^{2} e^{x}) = e^{x} (x^{2} + 2 x)

Factor out the common exponential term.

The derivative is eˣ(x² + 2x). Expanding it to x²eˣ + 2xeˣ gives the same function.

Common mistakes to check

Multiplying the derivatives

The derivative of a product is u′v + uv′, not u′v′.

Dropping the inner derivative

A chain-rule result must include the derivative of the inside function.

Substituting a point too early

Find the derivative function first, then evaluate it at the requested point.

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Questions students ask

What does a derivative measure?

It gives an instantaneous rate of change and, where the graph is smooth, the slope of the tangent line.

Can this calculator find higher derivatives?

Yes. State the derivative order, such as second derivative or third derivative, in the problem.

How do I find a derivative at a point?

Differentiate first, then substitute the point into the derivative if that derivative exists there.

Why can two derivative answers look different?

Factored and expanded expressions can be equivalent. Simplify both forms or expand them before comparing.