Free & Online Derivative Calculator (With Steps)

A derivative calculator is an online math tool that helps you find the derivative of a function easily and accurately. It is useful for students, teachers, engineers, and anyone studying calculus.

This calculator can solve:

• First derivatives
• Second derivatives
• Partial derivatives
• Directional derivatives
• Derivatives with steps

🔹 What Is a Derivative?

In calculus, a derivative measures how a function changes when its input changes. It tells us the rate of change of a function.

Example:$$f(x) = x^2$$$$f'(x) = 2x$$

This means the slope of the function at any point is 2x.

🔹 Derivative Calculator With Steps

Calculator with steps shows:

1. Original function
2. Applied rule (Power Rule, Chain Rule, etc.)
3. Final answer

This helps students understand how the solution is formed instead of just seeing the result.

🔹 Partial Derivative Calculator

A partial calculator is used for functions with more than one variable, such as:$$f(x, y) = x^2 + 3xy$$

Partial derivatives:$$\frac{\partial f}{\partial x} = 2x + 3y$$∂x∂f​=2x+3y $$\frac{\partial f}{\partial y} = 3x$$∂y∂f​=3x

This is common in physics, economics, and engineering.

🔹 Second Derivative Calculator

A second calculator finds the derivative of a derivative.

Example:$$f(x) = x^3$$

First derivative:$$f'(x) = 3x^2$$

Second derivative:$$f”(x) = 6x$$

Second derivatives are used to analyze:

• Acceleration
• Curve shape
• Maximum & minimum points

🔹 Directional Derivative Calculator

A directional derivative calculator measures the rate of change of a function in a specific direction.

Formula:$$D_{\vec{u}} f = \nabla f \cdot \vec{u}$$Du​f=∇f⋅u

It is used in:

• Vector calculus
• Physics
• Machine learning
• Optimization problems

Derivatives are widely used alongside Laplace transforms to solve differential equations in mathematics and engineering. Use our Laplace Transform Calculator for advanced calculus problems.

🔹 Why Use a Derivative Calculator?

✔ Saves time
✔ Avoids mistakes
✔ Shows steps
✔ Supports complex functions
✔ Mobile-friendly
✔ Student-friendly

🔹 Common Derivative Rules

Rule	Example
Power Rule	d/dx(xⁿ) = nxⁿ⁻¹
Constant Rule	d/dx(c) = 0
Sum Rule	d/dx(a+b) = a’+b’
Chain Rule	d/dx(f(g(x)))
Product Rule	d/dx(uv)

🔹 Who Should Use This Tool?

• Students
• Teachers
• Engineers
• Researchers
• Scientists

This derivative calculator makes calculus simple. Whether you need a partial derivative, second derivative, directional derivative, or a step-by-step solution, this tool provides fast and accurate results.

To learn more about derivatives, differentiation rules, limits, and applications of calculus, visit Paul’s Online Math Notes – Calculus.