Calculus
Partial Derivative Calculator
Compute partial derivatives of multivariable functions. Find the first and second-order partial derivatives of functions with two or more variables, treating other variables as constants.
d/dx
Examples:
Differentiation Rules
Power Rule
d/dx [x^n] = nx^(n-1)
Product Rule
[fg]' = f'g + fg'
Chain Rule
d/dx [f(g(x))] = f'(g(x))g'(x)
Constant Rule
d/dx [c] = 0
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Solution Methodology
01
Input Function
Enter the multivariable function f(x, y).
02
Select Variable
Choose which variable to differentiate with respect to.
03
Differentiate
Apply differentiation rules while holding other variables constant.
Common Questions
How do you take a partial derivative?
To take a partial derivative with respect to a specific variable (like x), you differentiate the function using normal rules while treating all other variables (like y and z) as if they were constant numbers.
What are mixed partial derivatives?
A mixed partial derivative is a second-order (or higher) derivative taken with respect to two different variables sequentially, such as differentiating by x, then by y. By Clairaut's theorem, under continuous conditions, the order does not matter: ∂²f/∂x∂y = ∂²f/∂y∂x.