A partial derivative calculator finds how a multivariable function changes with respect to one variable while the others stay constant. It’s a core tool in multivariable calculus, physics, economics and machine learning, and step-by-step solutions help you check homework and understand the process.
The rule is simple: treat every other variable as a constant and differentiate as usual. For f(x, y) = x²y + 3xy³, the partial derivative with respect to x is ∂f/∂x = 2xy + 3y³, because y acts like a constant. With respect to y, it’s ∂f/∂y = x² + 9xy². All the usual rules, like the product, quotient and chain rules, still apply.
Second-order partials take a partial derivative of a partial derivative. For the same function, ∂²f/∂x² = 2y, and the mixed partial ∂²f/∂x∂y = 2x + 9y². For most well-behaved functions, mixed partials are equal regardless of the order (Clairaut’s theorem), which is a handy way to check your work.
Where partial derivatives are used: finding the gradient (the direction of steepest increase), locating maximum and minimum points, building the Jacobian matrix, and computing rates of change in physics and economics. Common mistakes include forgetting to treat other variables as constants and mixing up the order of differentiation in notation.
Tips for getting accurate results from the Partial Derivative Calculator: double-check that every input uses the right units, enter numbers without commas or symbols, and run the calculation a second time with a quick estimate in your head to confirm the answer looks reasonable.
How to use the Partial Derivative Calculator on Minedit: enter your values in the fields, press calculate, and review the step-by-step breakdown under the result. If something looks off, change one input at a time to see how it affects the answer, which is also a great way to learn the math behind it.
Learn more on Wikipedia’s partial derivative article. Find Jacobian, double integral and implicit differentiation calculators on Minedit.