How partial derivatives differ
- Choose the variable first, such as \(x\), \(y\), or \(z\).
- Hold every other variable constant during differentiation.
- Repeat with another variable if you need the full gradient.
Partial Derivative Calculator
Find partial derivatives for multivariable expressions.
Use this calculator as a study checker
Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.
- Check the method before copying the answer.
- Use the examples below to test nearby problems.
- Read the calculus guides for worked explanations.
Solution
50 study checks todayEnter an expression or choose an example to calculate.
Partial Derivative Examples
What this calculator is for
A partial derivative measures how a multivariable function changes with respect to one variable while the other variables are held constant. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.
Manual example
- Problem: find \(\partial/\partial x\) of \(x^2y+3y\).
- Treat \(y\) as a constant: \(\partial(x^2y)/\partial x=2xy\).
- The term \(3y\) is constant with respect to \(x\), so the result is \(2xy\).
Common mistakes to avoid
- Differentiating every variable at once.
- Treating \(y\) as a function of \(x\) when the task is partial differentiation.
- Not specifying the variable.
When to double-check the result
For implicit relationships between variables, use the implicit derivative calculator instead of treating variables as independent.