How gradients are assembled
- Take the partial derivative with respect to each variable.
- Place the results in vector order, usually \(\langle f_x,f_y,f_z\rangle\).
- Interpret the vector as the direction of fastest increase.
Gradient Calculator
Calculate the gradient vector of a multivariable function.
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.
Gradient Examples
What this calculator is for
The gradient is a vector made from partial derivatives. It points in the direction where a function increases fastest. 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: \(f(x,y)=x^2+y^2\).
- Partial derivatives are \(f_x=2x\) and \(f_y=2y\).
- So \(\nabla f=\langle2x,2y\rangle\).
Common mistakes to avoid
- Returning a scalar instead of a vector.
- Changing the order of vector components.
- Treating other variables as functions instead of constants.
When to double-check the result
For constrained optimization, the gradient is only one part of the method; include the constraint separately.