Compute partial derivatives with step-by-step solutions
Differentiate with respect to: x
∂/∂x (y²) = 0 (treat y as constant)
∂/∂x (x² + y²) = 2x + 0
About Partial Derivatives
Important Notes
When computing partial derivatives, remember to treat all other variables as constants. Our calculator handles this automatically, providing step-by-step solutions for better understanding.
What is a Partial Derivative?
A partial derivative of a function of multiple variables is its derivative with respect to one of those variables, with all other variables held constant. It measures how the function changes as only that variable changes.
Notation
Partial derivatives are denoted by ∂ (the partial derivative symbol). For a function f(x,y), the partial derivative with respect to x is written as ∂f/∂x or fₓ.
Applications
Partial derivatives are essential in multivariable calculus, physics, engineering, economics, and machine learning for optimization, gradient descent, and understanding multivariable systems.
Partial Derivative Calculator
Our partial derivative calculator helps you compute partial derivatives step by step. Whether you need to find partial derivatives with respect to x, y, or any other variable, our tool provides accurate results with detailed explanations.
How to Use the Partial Derivative Calculator
Simply enter your multivariable function, select the variable you want to differentiate with respect to, and click calculate. Our calculator will show you the partial derivative along with step-by-step solutions.
Partial Derivative Examples
Examples of partial derivatives include calculating ∂/∂x of functions like x² + y², sin(xy), or e^x + ln(y). Our calculator handles all these cases and more.
Multivariable Calculus Tools
In addition to partial derivatives, our calculator can help with other multivariable calculus concepts like gradient, directional derivatives, and optimization problems.
Free Online Math Calculator
This free online partial derivative calculator is perfect for students, teachers, and professionals who need to compute partial derivatives quickly and accurately.
Step-by-Step Solutions
Unlike other calculators that only give the final answer, our partial derivative calculator provides detailed step-by-step solutions to help you understand the process.